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More Recently modified knowls
A
curve.highergenus.aut.group_action A group acting on a compact Riemann Surface
lfunction.history A history of L-functions
group.a_group A-group
group.abelian Abelian group
ag.abelian_surface Abelian surface
ag.abelian_variety Abelian variety
varieties.about About varieties
g2c.abs_discriminant Absolute discriminant
group.galois.absolute Absolute Galois group
nf.absolute_value Absolute value of a field
ec.additive_reduction Additive reduction
ag.affine_space Affine space
nf.algebraic_closure Algebraic closure of a field
ag.curve Algebraic curve
mf.gl2.history.varieties Algebraic varieties
ag.variety Algebraic variety
group.almost_simple Almost simple group
group.alternating Alternating group
nf.class_number_formula Analytic class number formula
ec.analytic_sha_order Analytic order of Ш
ec.q.analytic_sha_order Analytic order of Ш
g2c.analytic_sha Analytic order of Sha
ec.q.analytic_sha_value Analytic order of Sha (numerical value)
cmf.analytic_rank Analytic rank
lfunction.analytic_rank Analytic rank
g2c.analytic_rank Analytic rank of a curve
av.fq.angle_rank Angle rank of a set
lfunction.arithmetic Arithmetic L-function
nf.arithmetically_equivalent Arithmetically equivalent fields
gg.arithmetically_equivalent Arithmetically equivalent siblings
cmf.artin_field Artin field
cmf.artin_image Artin image
artin.lfunction Artin L-function
lfunction.history.artin Artin L-functions
ring.associate Associate of an element
alg.binary_operation.associative Associative binary operation
nf.assuming_grh Assuming GRH
cmf.atkinlehner Atkin-Lehner eigenvalue
curve.highergenus.aut.characters Automorphism group characters
lattice.automorphism_group Automorphism group of an integral lattice
group.automorphism Automorphisms of a group
mf.siegel.extent.kp Available samples for $M_2(K(p))$
B
cmf.bad_prime Bad prime
ag.base_change Base change
ec.base_change Base change
ag.base_field Base field
belyi.base_field Base field of a Belyi map
mf.bianchi.base_change Base-change Bianchi modular forms
character.dirichlet.basic_properties Basic properties of Dirichlet characters
belyi.galmap Belyi map
belyi.label Belyi map label
af.bernoulli_numbers Bernoulli numbers
hgm.bezout_determinant Bezout determinant
alg.bezout_matrix Bezout matrix
mf.bianchi.bianchigroup Bianchi Groups
mf.bianchi.bianchimodularforms Bianchi modular forms
mf.bianchi.newform Bianchi newform
alg.binary_operation Binary operation
ec.q.galois_rep_image_borel Borel case
gl2.borel Borel subgroup
curve.highergenus.aut.braid_equivalence Braid Equivalence
curve.highergenus.aut.branchpoints Branch Points
g2c.bsd_invariants BSD invariants
stats.buckets Buckets for statistics
C
ec.q.canonical_height Canonical height
gl2.cartan Cartan subgroup
lattice.catalogue_of_lattices Catalogue of Lattices
group.center Center of a group
lfunction.central_character Central character of an L-function
lfunction.central_point Central point of an L-function
group.central Central subgroup
lfunction.central_value Central value of an L-function
group.centralizer Centralizer of a subgroup
group.subgroup.centralizer Centralizer of a subgroup
group.representation.character Character of a group representation
mf.maass.mwf.character Character of a Maass form
gg.character_table.data Character table data
ring.characteristic Characteristic of a ring
group.characteristic_subgroup Characteristic subgroup
group.chief_series Chief series of a group
ag.cluster_picture Cluster picture
mf.bianchi.cm CM Bianchi newforms
ag.cm_field CM field
cmf.cm_form CM form
nf.cm_field CM number field
cmf.minimal_twist cmf.minimal_twist
cmf.coefficient_field Coefficient field for newforms
lfunction.coefficient_field Coefficient field of an L-function
cmf.coefficient_ring Coefficient ring
cmf.hecke_ring_generators Coefficient ring generator bound
mf.gl2.history.combinatorics Combinatorics and $q$-series
alg.binary_operation.commutative Commutative binary operation
group.commutator_subgroup Commutator subgroup of a group
lfunction.completed Completed L-function
rcs.cande.lfunction Completeness of L-function Data
group.complex_character_table Complex character table of a finite group
nf.complex_embedding Complex embedding
cmf.embedding_label Complex embedding label
ag.complex_multiplication Complex multiplication
ec.complex_multiplication Complex multiplication
st_group.component_group Component group of a Sato-Tate group
st_group.components Components of a Sato-Tate group
g2c.conditional_mw_group Conditional Mordell-Weil group
character.dirichlet.conductor Conductor of a Dirichlet character
character.dirichlet.conrey.conductor Conductor of a Dirichlet character from its Conrey label
lfunction.conductor Conductor of an L-function
ec.conductor_valuation Conductor valuation
mf.bianchi.bianchicongruencesubgroup Congruence subgroup of a Bianchi group
data.congruent_numbers Congruent numbers data
gg.conjugacy_classes Conjugacy class
group.conjugacy_class Conjugacy class
gg.conjugacy_classes.data Conjugacy class representatives
curve.highergenus.aut.conjugacyclasses Conjugacy classes
st_group.connected Connected Sato-Tate group
character.dirichlet.conrey.index Conrey index of a Dirichlet character
character.dirichlet.conrey Conrey label of Dirichlet characters
character.dirichlet.conrey.primitive_generator Conrey primitive generator modulo $p$
artin.permutation_container Containing permutation representation
group.core Core of a subgroup
av.fq.frobenius_angles_correctness Correctness of Frobenius angles
group.coset Coset of a subgroup
doc.create_knowl Create a knowl
ec.q.cremona_label Cremona label
lfunction.critical_line Critical line of an L-function
lfunction.critical_strip Critical strip
crystals.crystal Crystal
hgm.cusp_index Cusp index
cmf.cusp_form Cuspidal modular form
group.cyclic Cyclic group
ag.cyclic_trigonal Cyclic trigonal curve
D
clusterpicture.data Data for a cluster picture
character.dirichlet.data Data for a dirichlet character
character.dirichlet.orbit_data Data for a Galois orbit of Dirichlet characters
lf.field.data Data for a local field
group.small.data Data on small group
cmf.decomposition.new.gamma0chi Decomposition into newforms
cmf.dim_decomposition Decomposition into newforms
cmf.decomposition.new.gamma1 Decomposition into newforms for Gamma1(N)
ring.dedekind_domain Dedekind domain
mf.half_integral_weight.dedekind_eta Dedekind eta function
lfunction.history.dedekind Dedekind zeta-functions, history
cmf.defining_polynomial Defining polynomial
lf.defining_polynomial Defining polynomial of a local field
nf.defining_polynomial Defining Polynomial of a Number Field
gg.degree Degree
lfunction.known_degree1 Degree 1 L-functions, all
lfunction.known_degree2 Degree 2 L-functions, examples
lfunction.known_degree3 Degree 3 L-functions, examples
lfunction.known_degree4 Degree 4 L-functions, examples
belyi.degree Degree of a Belyi map
character.dirichlet.degree Degree of a Dirichlet character
st_group.degree Degree of a Sato-Tate group
lfunction.degree Degree of an L-function
group.derived_series Derived series of a group
doc.knowl.description Description field in knowls
cmf.statistics_extent Description of completeness
doc.development Developers Guide
group.dicyclic Dicyclic group
group.dihedral Dihedral group
cmf.dimension Dimension
cmf.display_dim Dimension
curve.highergenus.aut.dimension Dimension of a family of curves
cmf.dimension_galois_orbit Dimension of a Hecke orbit
mf.hilbert.dimension Dimension of a Hecke orbit
cmf.atkin_lehner_dims Dimensions of Atkin-Lehner subspaces
group.direct_product Direct product of groups
character.dirichlet Dirichlet character
dq.character.dirichlet.extent Dirichlet character data extent
character.dirichlet.group Dirichlet character group
lfunction.dirichlet Dirichlet L-function
lfunction.dirichlet_series Dirichlet series
lfunction.history.dirichlet Dirichlet's work on L-functions
lf.discriminant_exponent Discriminant exponent of a local field
nf.poly_discriminant Discriminant of polynomial
lf.discriminant_root_field Discriminant root field of a local field
ec.discriminant_valuation Discriminant valuation
cmf.distinguishing_primes Distinguishing Hecke operators
af.divisor_function Divisor function
cmf.dualform Dual cuspform
lattice.dual Dual lattice
lfunction.dual Dual of an L-function
mf.siegel.lift.ikeda Duke-Imamoglu-Ikeda lift
E
lf.eisenstein_polynomial Eisenstein polynomial
ec.q.invariants Elliptic curve invariants
mf.gl2.history.elliptic Elliptic functions
gg.elusive_group Elusive group
cmf.embedding_format Embedding Format
ag.endomorphism_algebra Endomorphism algebra
g2c.end_alg Endomorphism algebra
av.endomorphism_field Endomorphism field
g2c.jac_endomorphisms Endomorphism invariants
g2c.jac_end_lattice Endomorphism lattice
ag.endomorphism_ring Endomorphism ring
cmf.eta_quotient Eta quotient
ring.euclidean_domain Euclidean domain
g2c.bad_lfactors Euler factors at bad primes
specialfunction.gamma Euler gamma function
lfunction.riemann.euler_product Euler product for the Riemann zeta function
lfunction.euler_product Euler product of an L-function
lfunction.history.euler Euler's work on the zeta function
st_group.probabilities Event probabilities
ec.q.galois_rep_image_exc Exceptional case
gl2.exceptional Exceptional subgroup
doc.view_knowl Expand a knowl
group.exponent Exponent of a group
dq.hecke_algebras.extent Extent of data for Hecke Algebras
F
ring.field Field
character.dirichlet.value_field Field of values of a Dirichlet character
field.about Fields
belyi.search_input Find a Belyi map
mf.bianchi.search_input Find a Bianchi modular form
character.dirichlet.search_input Find a Dirichlet character
curve.highergenus.aut.search_input Find a family of higher genus curves
gg.search_input Find a Galois group
g2c.search_input Find a genus 2 curve
hgm.search_input Find a hypergeometric motive
nf.search_input Find a number field
lf.search_input Find a p-adic field
st_group.search_input Find a Sato-Tate group
artin.search_input Find an Artin representation
ec.q.search_input Find an elliptic curve
ec.search_input Find an elliptic curve
lattice.search_input Find an integral lattice
mf.hilbert.search_input Find Hilbert modular form by label
group.fitting_subgroup Fitting subgroup of a group
character.dirichlet.field_cut_out Fixed field of a Dirichlet character
cmf.fouriercoefficients Fourier coefficients of a modular form
mf.maass.picard.fourierexpansion Fourier expansion of a Maass form on PSL(2,Z[i])
mf.maass.mwf.fourierexpansion Fourier expansion of Maass form
ring.fractional_ideal Fractional ideal
group.frattini_subgroup Frattini subgroup of a group
ec.q.frey Frey curve
av.fq.frobenius_angles Frobenius angles
nf.frobenius_cycle_types Frobenius cycle types
artin.frobenius_schur_indicator Frobenius-Schur indicator of a representation
group.fuchsian Fuchsian group
curve.highergenus.aut.full Full group of automorphisms
av.fq.class_number_1 Function fields of class number 1
lfunction.functional_equation Functional equation of an L-function
group.fuchsian.fundamental_domain Fundamental domain
group.sl2z.fundamental_domain Fundamental domain of $\SL(2,\Z)$
G
nf.galois_closure Galois closure of an extension
cmf.galois_conjugate Galois conjugate newforms
gg.galois_group Galois group
nf.galois_group Galois group
nf.galois_group.data Galois group information
lf.galois_invariants Galois invariants of a local field
lf.galois_mean_slope Galois mean slope
nf.galois_group.gmodule Galois module information
mf.siegel.galois_orbit Galois orbit
cmf.hecke_galois_orbit Galois orbit label
character.dirichlet.galois_orbit Galois orbit of a Dirichlet character
cmf.galois_orbit Galois orbit of a newform
cmf.galois_representation Galois representation
lf.galois_splitting_model Galois splitting model of a local field
lfunction.gamma_factor Gamma factors
character.dirichlet.gauss_sum Gauss sum
group.generalized_quaternion Generalized quaternion
curve.highergenus.aut.generatingvector Generating Vector
nf.field_generator Generator of a number field
character.dirichlet.group.generators Generators of a Dirichlet character group
group.generators Generators of a group
st_group.generators Generators of a Sato-Tate group
lmfdb.object_information Generic dynamic knowl
g2c.g2curve Genus 2 curve
belyi.genus Genus of a Belyi map
ag.curve.genus Genus of a smooth curve
group.sl2z.genus_subgroup Genus of a subgroup of the modular group
g2c.geom_aut_grp Geometric automorphism group
ag.geom_endomorphism_algebra Geometric endomorphism algebra
ag.geom_endomorphism_ring Geometric endomorphism ring
ec.geom_endomorphism_ring Geometric endomorphism ring
g2c.geometric_invariants Geometric invariants
ag.geom_simple Geometrically simple
av.geometrically_simple Geometrically simple
belyi.geometry_type Geometry type of a Belyi map
ec.global_minimal_model Global minimal model
ec.good_ordinary_reduction Good ordinary reduction
ec.good_reduction Good reduction
ec.good_supersingular_reduction Good supersingular reduction
lattice.gram Gram matrix
mf.siegel.lift.gritsenko Gritsenko lift
gg.group_action_invariants Group action Invariants
curve.highergenus.aut.groupalgebradecomp Group algebra decomposition of Jacobian varieties
group.homomorphism Group homomorphism
gg.invariants Group invariants
group.isomorphism Group isomorphism
group.about Groups
doc.knowl.annotation_guidelines Guidelines for writing annotations
H
mf.half_integral_weight Half-integral weight modular forms
group.subgroup.hall Hall subgroup
g2c.has_square_sha Has square Ш
combin.hasse_diagram Hasse diagram
g2c.hasse_weil_conjecture Hasse-Weil conjecture
lfunction.history.hasse_weil Hasse-Weil L-function
hecke_algebra.definition Hecke algebra
mf.bianchi.hecke_algebra Hecke algebra
character.hecke Hecke character
cmf.heckecharpolys Hecke characteristic polynomial
mf.gl2.history.hecke Hecke Characters
mf.hilbert.eigenvalue Hecke eigenvalues
cmf.hecke_kernels Hecke kernel
lfunction.history.hecke_characters Hecke L-functions
cmf.hecke_operator Hecke operator
lfunction.history.hecke_operators Hecke operators, history
cmf.hecke_orbit Hecke orbit
mf.hilbert.hecke_orbit Hecke orbit for Hilbert modular form
lattice.hermite_number Hermite number
hgm.field.label HGM Labels
crystals.highest_weight Highest weight crystals
lattice.history History of Lattices
av.fq.honda_tate Honda-Tate Theorem
content.how_to_cite How to cite the LMFDB
curve.highergenus.hurwitz_bound Hurwitz bound
mf.bianchi.hyperbolic3space Hyperbolic 3-space
ag.hyperelliptic_curve Hyperelliptic curve
I
nf.ideal_labels Ideal labels
ring.ideal Ideal of a ring
doc.knowl.identifier Identifier of a knowl
st_group.identity_component Identity component of a Sato-Tate group
alg.binary_operation.identity Identity for a binary operation
g2c.igusa_clebsch_invariants Igusa-Clebsch invariants of a genus 2 curve
ec.q.galois_rep_image Image of mod p Galois Representation
artin.gg_quotient Image of the representation
doc.knowl.implicit Implicit creation of knowls
cmf.include_all_spaces Include all spaces
group.subgroup.index Index of a subgroup
intro.description Index page, first sentences
character.dirichlet.induce Induced Dirichlet character
lf.inertia_group Inertia group
mf.gl2.history.infinite Infinite products
av.fq.initial_coefficients Initial coefficients of the L-polynomial
group.inner_automorphism Inner automorphism of a group
cmf.inner_twist Inner twist
cmf.inner_twist_count Inner twist count
cmf.inner_twist_group Inner twist group
cmf.inner_twist_multiplicity Inner twist multiplicity
cmf.inner_twist_proved Inner twist proved
gg.arithmetically_equiv_input Input for arithmetically equivalent fields
ring.integral_domain Integral domain
nf.integral Integral elements
lattice.definition Integral Lattice
ec.integral_model Integral model
ec.q.integral_points Integral points
ring.integrally_closed Integrally closed
lf.intermediate_fields Intermediate fields
nf.intermediate_fields Intermediate fields
intro Introduction
intro.features Introduction/Features
lfunction.invariants Invariants of an L-function
alg.binary_operation.inverse Inverse for a binary operation
ring.irreducible Irreducible element
ag.irreducible Irreducible variety
nf.is_galois Is a Galois extension
av.fq.abvar.data Isogeny class data
ec.isogenygraph.legend Isogeny graph legend
ec.weierstrass_isomorphism Isomorphism between Weierstrass models
J
ec.j_invariant_denominator_valuation j-invariant denominator valuation
mf.jacobi Jacobi forms
character.dirichlet.jacobi_sum Jacobi sum
character.dirichlet.jacobi_symbol Jacobi symbol
ag.jacobian Jacobian of a curve
av.fq.jacobian Jacobian of a curve
K
lattice.kissing Kissing number
character.dirichlet.kloosterman_sum Kloosterman sum
doc.knowl Knowl
doc.knowl.guidelines Knowl Edit Guidelines
test.knowlparam Knowl with parameters
g2c.known_rational_points Known rational points
ec.kodaira_symbol Kodaira symbol
ec.q.kodaira_symbol Kodaira symbol
character.dirichlet.kronecker_symbol Kronecker symbol
L
lfunction L-function
lfunction.spectral_parameters L-function spectral parameters
lfunction.about L-functions
lfunction.history.maass L-functions of Maass forms
group.label_conjugacy_class Label of a complex conjugacy class
character.dirichlet.galois_orbit_label Label of a Galois orbit of a Dirichlet character
group.label_complex_group_char Label of irreducible complex characters of groups
lfunction.history.langlands_program Langlands program
lfunction.leading_coeff Leading coefficient
lfunction.degree2holo.key Legend for GL(2) holomorphic graph of dots
character.dirichlet.legendre_symbol Legendre symbol
mf.hilbert.level_norm Level of a Hilbert modular form
mf.siegel.lift Lift Siegel modular form
crystals.littelmann_path Littelmann path model for crystals
doc.lmfdb.improve LMFDB backend
doc.news.in_the_news LMFDB in the news
lf.algebra.data Local algebra
nf.local_algebra Local algebra
lf.local_field Local field
lf.invariants Local field invariants
g2c.local_invariants Local invariants
g2c.good_lfactors Local L-factors at good primes
ec.local_minimal_discriminant Local minimal discriminant of an elliptic curve
ec.local_minimal_model Local minimal model
ec.local_root_number Local root number
g2c.locally_solvable Locally solvable
group.lower_central_series Lower central series of a group
M
mf.maass.mwf.coefficients Maass form coefficients
mf.maass.mwf.plot Maass form plot
mf.maass.mwf.weight0 Maass forms of weight 0
mf.maass.picard Maass forms on PSL(2,Z[i])
content.edit_board Management board
ec.maximal_galois_rep Maximal Galois representation
ring.maximal_ideal Maximal ideal
group.maximal_subgroup Maximal subgroup of a group
st_group.subgroups Maximal subgroups
group.metabelian Metabelian group
group.metacyclic Metacyclic group
character.dirichlet.minimal Minimal Dirichlet character
ec.minimal_discriminant Minimal discriminant
ag.minimal_field Minimal field of definition
cmf.minimal Minimal modular form
nf.minimal_polynomial Minimal polynomial
st_group.supgroups Minimal supergroups
lattice.minimal_vector Minimal vector length
ec.q.minimal_weierstrass_equation Minimal Weierstrass equation over $\mathbb Q$
cmf.minus_space Minus space
mf.siegel.lift.miyawaki Miyawaki lift
mf.siegel.lift.miyawaki2 Miyawaki lift of type II
ag.modcurve.x0 Modular curve $X_0(N)$
ag.modcurve.x1 Modular curve $X_1(N)$
mf.about Modular Forms
character.dirichlet.modulus Modulus of a Dirichlet character
st_group.moments Moment statistics
curve.highergenus.aut.monodromy Monodromy Group
group.monomial Monomial group
nf.monomial_order Monomial order
g2c.mw_generator Mordell-Weil generator
ec.mw_generators Mordell-Weil generators
ec.mordell_weil_group Mordell-Weil group
g2c.mordell_weil_rank Mordell-Weil rank
ec.mordell_weil_theorem Mordell-Weil theorem
motives.about Motives
lfunction.motivic_weight Motivic weight
nf.multiplicative_gal_module Multiplicative Galois Module Structure
ec.multiplicative_reduction Multiplicative reduction
mf.maass.mwf.dimension Multiplicity of an eigenvalue
mf.multipliersystem Multiplier system
N
lattice.name Name of a lattice
doc.knowl.naming_conventions Naming conventions for knowls
doc.knowl.naming_suggestions Naming suggestions
nf.narrow_class_group Narrow class group
nf.narrow_class_number Narrow class number
cmf.newform Newform
cmf.newform_subspace Newform subspace
lf.newton_polygon Newton polygon of a polynomial
group.nilpotent Nilpotent group
cmf.nk2 Nk^2
ring.noetherian Noetherian ring
ec.q.galois_rep_image_nsp_cartan Non-split Cartan case
gl2.nonsplit_cartan Non-split Cartan subgroup
group.nonsplit_product Non-split extension of groups
ec.nonsplit_multiplicative_reduction Non-split multiplicative reduction
ec.q.non-surjective_prime Non-surjective prime
cmf.nontrivial_twist Nontrivial inner twist
ec.discriminant_norm Norm of discriminant
group.subgroup.normal_closure Normal closure of a subgroup
group.normal_series Normal series of a group
group.subgroup.normal Normal subgroup of a group
lfunction.normalization Normalization of an L-function
nf.defining_polynomial.normalization Normalization of defining polynomials for number fields
lattice.normalized_minimal_vector Normalized minimal vector of a lattice
gl2.normalizer_cartan Normalizer of a Cartan subgroup
gl2.normalizer_nonsplit_cartan Normalizer of a non-split Cartan subgroup
gl2.normalizer_split_cartan Normalizer of a split Cartan subgroup
group.subgroup.normalizer Normalizer of a subgroup
ec.q.galois_rep_image_norm_nsp_cartan Normalizer of the nonsplit Cartan case
ec.q.galois_rep_image_norm_sp_cartan Normalizer of the split Cartan case
nf.invariants Number field invariants
character.dirichlet.related_fields Number fields related to a Dirichlet character
belyi.num_orbits Number of Galois orbits
av.hyperelliptic_count Number of hyperelliptic Jacobians
av.jacobian_count Number of Jacobians
g2c.num_rat_pts Number of rational points
O
cmf.decomposition.old.gamma1 Oldspace decomposition for Gamma1(N)
cmf.decomposition.old.gamma0chi Oldspace decomposition for newform space
character.dirichlet.galois_orbit_index Orbit index of a Dirichlet character
belyi.orbit_size Orbit size
nf.order Order
character.dirichlet.order Order of a Dirichlet character
character.dirichlet.conrey.order Order of a Dirichlet character from its label
character.dirichlet.group.order Order of a Dirichlet character group
group.order Order of a group
group.element_order Order of a group element
g2c.mw_generator_order Order of a Mordell-Weil generator
av.fq.ordinary Ordinary
group.outer_aut Outer automorphism group
P
av.fq.p_rank p-rank
g2c.paramodular_conjecture Paramodular conjecture
group.paramodular Paramodular group
mf.siegel.newform.paramodular Paramodular newform
character.dirichlet.parity Parity of a Dirichlet character
character.dirichlet.conrey.parity Parity of a Dirichlet character from its Conrey label
belyi.passport Passport
group.perfect Perfect groups
cmf.petersson_scalar_product Petersson scalar product
cmf.plus_space Plus space
mf.gl2.history.poincare Poincaré series
specialfunction.poincare Poincaré series
ag.fq.point_counts Point counts of a variety
av.fq.curve_point_counts Point counts of the curve
av.polarization Polarization
lattice.postive_definite Positive definite lattice
av.potential_toric_rank Potential toric rank
doc.lmfdb.contextualize Presentation of the data in the LMFDB
ring.prime_ideal Prime ideal
ag.bad_prime Prime of bad reduction
ag.good_prime Prime of good reduction
ag.good_reduction Primes of good reduction
g2c.good_reduction Primes of good reduction
ag.potential_good_reduction Primes of potential good reduction
character.dirichlet.primitive Primitive Dirichlet character
nf.primitive_element Primitive element
lattice.primitive Primitive integral lattice
lfunction.primitive Primitive L-function
character.dirichlet.principal Principal Dirichlet character
ring.principal_fractional_ideal Principal fractional ideal
ring.principal_ideal_domain Principal ideal domain
av.princ_polarizable Principally polarizable
artin.projective_field Projective Artin field
cmf.projective_field Projective field
cmf.projective_image Projective image
artin.projective_image_type Projective image type
ag.projective_space Projective space
stats.proportions Proportions for statistics
Q
mf.hilbert.q_expansion q-expansion of a Hilbert modular form
mf.quasi_modular Quasi-modular form
group.quasisimple Quasisimple group
ag.quotient_curve Quotient curve
curve.highergenus.aut.quotientgenus Quotient genus
group.quotient Quotient group
R
group.radical Radical of a group
lfunction.history.ramanujan_tau Ramanujan tau L-function
belyi.ramification_type Ramification type
lfunction.history.rankin_selberg Ranking-Selberg convolution, history
group.rational_group Rational group
lfunction.rational Rational L-function
g2c.all_rational_points Rational points
st_group.rational Rational Sato-Tate group
st_group.real_dimension Real dimension of a Sato-Tate group
character.dirichlet.real Real Dirichlet character
nf.real_embedding Real embedding
ag.real_endomorphism_algebra Real endomorphism algebra
ag.real_geom_endomorphism_algebra Real geometric endomorphism algebra
ag.real_multiplication Real multiplication
cmf.rm_form Real multiplication
ec.q.real_period Real period
g2c.real_period Real period
ec.reduction_type Reduction type
curve.highergenus.aut.refinedpassport Refined passport
doc.related_to Related objects
cmf.relative_dimension Relative dimension
dq.mf.bianchi.reliability Reliability of Bianchi Modular Form data
rcs.rigor.lfunction.curve Reliability of Curve L-function Data
rcs.rigor.character.dirichlet Reliability of Dirichlet Character Data
rcs.rigor.lfunction.dirichlet Reliability of Dirichlet L-function Data
rcs.rigor.lfunction.maass Reliability of Maass form L-function data
rcs.rigor.lfunction.modular Reliability of Modular L-function Data
mf.gl2.history.remainder Remainder terms
doc.knowl.rename Renaming a knowl
repn.about Representation
lf.residue_field Residue field
lf.residue_field_degree Residue field degree of a local field
ag.riemann_surface Riemann surface
lfunction.riemann Riemann zeta-function
lfunction.history.riemanns_memoir Riemann's memoir
lf.ring_of_integers Ring of integers of a local field
character.dirichlet.roadmap Roadmap for Dirichlet characters
lfunction.roadmap Roadmap for L-functions
mf.maass.roadmap Roadmap for Maass forms
cmf.root Root
lattice.root_lattice Root lattice
ec.q.rouse_classification Rouse classification
ec.rouse_label Rouse label
S
sage.cellexample Sage cell example
sage.test Sage cell knowl
mf.siegel.lift.saito_kurokawa Saito-Kurokawa lift
cmf.satake_parameters Satake parameters
st_group.definition Sato-Tate group
ag.sato_tate_group Sato-Tate group (of a motive)
g2c.st_group_identity_component Sato-Tate group identity component
st_group.invariants Sato-Tate group invariants
st_group.label Sato-Tate group labels
st_group.roadmap Sato-Tate group roadmap
st_group.subsupgroups Sato-Tate subgroups and supergroups
lfunction.selberg_class.axioms Selberg class axioms
lfunction.selberg_class Selberg class of L-functions
cmf.selfdual Self dual modular form
cmf.self_twist_field Self twist field
mf.ellitpic.self_twist Self twist of a modular form
lfunction.self-dual Self-dual L-function
cmf.self_twist Self-twist
ec.semi_global_minimal_model Semi-global minimal model
av.semiabelian_variety Semiabelian variety
group.semidirect_product Semidirect product of groups
ec.q.semistable Semistable elliptic curve
nf.separable_algebra Separable algebra
nf.separable Separable extension
nf.serre_odlyzko_bound Serre Odlyzko bound
cmf.shimura_correspondence Shimura correspondence
mf.half_integral_weight.shimura_decomposition Shimura decomposition
ag.shimura_variety Shimura Variety
gg.other_representations Siblings for a Galois group
mf.siegel.phi Siegel $\Phi$ operator
mf.siegel.cusp_form Siegel cusp form
mf.siegel.eisenstein_series Siegel Eisenstein series
mf.siegel.klingen_eisenstein_series Siegel Klingen-Eisenstein series
mf.siegel.hecke_operator Siegel modular form Hecke operators
lfunction.history.siegel Siegel modular forms, history
mf.siegel.halfspace Siegel upper half space
mf.bianchi.sign Sign of a Bianchi newform
lfunction.root_number Sign of an L-function
curve.highergenus.aut.signature Signature of a group action on a curve
lfunction.signature Signature of an L-function
ag.simple Simple
gg.simple_name Simple group name
group.simple Simple groups
g2c.simple_equation Simplified equation
group.socle Socle of a group
group.solvable Solvable group
cmf.sort_order Sort order
rcs.groups.abstract.source Source of abstract group data
dq.belyi.source Source of Belyi maps data
rcs.source.character.dirichlet Source of Dirichlet character computations
rcs.source.lfunction.dirichlet Source of Dirichlet L-function Data
rcs.source.lfunction.curve Source of L-function Data
dq.lattice.source Source of lattice data
rcs.source.maass Source of Maass forms data
rcs.source.lfunction.maass Source of Maass L-function Data
rcs.source.lfunction.modular Source of Modular L-function Data
rcs.source.zeros.zeta Source of Riemann Zeta Zeros Data
rcs.source.st_group Source of Sato-Tate Group Data
cmf.newspace Space of newforms
cmf.newspaces Space of newforms
ec.q.galois_rep_image_sp_cartan Split Cartan case
gl2.split_cartan Split Cartan subgroup
ec.split_multiplicative_reduction Split multiplicative reduction
ag.splitting_field Splitting field
curve.highergenus.aut.generators Standard generators
character.dirichlet.group.structure Structure of a Dirichlet group
cmf.sturm_bound Sturm bound
cmf.sturm_bound_gamma1 Sturm bound for $\Gamma_1(N)$
gg.subfields Subfields
group.subgroup.diagram Subgroup diagram
group.subgroup.diagram.lmfdb Subgroup diagrams in the LMFDB
group.subgroup Subgroup of a group
gg.subnormal_series Subnormal series
av.fq.supersingular Supersingular abelian variety
group.supersolvable Supersolvable group
ec.q.surjective_prime Surjective prime
group.sylow_subgroup Sylow subgroup
group.symmetric Symmetric group
group.sp2gr Symplectic group
T
zeros.first.contents Table of first zeros of L-function
ec.tamagawa_number Tamagawa number
g2c.tamagawa Tamagawa numbers
ec.padic_tate_module Tate module of an elliptic curve
lfunction.history.tates_thesis Tate's thesis
ag.tate_shafarevich Tate-Shafarevich group
lfunction.taxonomy Taxonomy of L-functions
test.text test
users.edgarcosta.note test
test.suggestions Test knowl suggestions
mf.maass.mwf.eigenvalue The eigenvalue of a Maass form
mf.maass.mwf.level The level of a Maass form
mf.maass.mwf.ncoefficients The number of coefficients
mf.maass.mwf.precision The precision of an eigenvalue
mf.maass.mwf.spectralparameter The spectral parameter of a Maass waveform
mf.maass.mwf.symmetry The symmetry of a Maass form
lf.unramified_totally_ramified_tower The unramified/totally ramified tower of a local field
mf.maass.mwf.weight The weight of a Maass form
mf.siegel.theta_constant Theta constant
mf.half_integral_weight.theta Theta function
mf.gl2.history.theta Theta functions
dq.zeros.zeta.toomany Too many zeros
curve.highergenus.aut.topological_equivalence Topological Equivalence
group.torsion Torsion group
ec.q.torsion_growth Torsion growth in number fields
g2c.torsion_order Torsion order
g2c.torsion Torsion subgroup
nf.totally_imaginary Totally imaginary
nf.totally_positive Totally positive
nf.totally_real Totally real
stats.totals Totals for statistics
cmf.trace_bound Trace bound
cmf.space_trace_form Trace form
cmf.trace_form Trace form
st_group.trace_moments Trace moments of a Sato-Tate group
artin.trace_of_complex_conj Trace of complex conjugation
st_group.trace_zero_density Trace zero density of a Sato-Tate group
doc.knowl.context_free Transclusion (definition)
mf.transformation_property Transformation property for modular forms
belyi.permutation_triple Transitive permutation triple
lfunction.trivial_zero Trivial zeros of an L-function
nf.sextic_twin Twin sextic algebra
cmf.twist Twist
cmf.twist_minimal Twist minimal
cmf.twist_multiplicity Twist multiplicity
U
lfunction.underlying_object Underlying object of an L-function
lattice.unimodular Unimodular lattice
ring.unique_factorization_domain Unique factorization domain
nf.torsion Unit group torsion
ring.unit Unit in a ring
lf.unramified_degree Unramified degree of a local field
lf.unramified_subfield Unramified subfield
doc.upload_data Upload data
group.upper_central_series Upper central series of a group
mf.upper_half_plane Upper half-plane
V
character.dirichlet.values Values of a Dirichlet character
character.dirichlet.values_on_gens Values of a Dirichlet character on generators
mf.siegel.vector_valued Vector-valued Siegel modular forms
W
ec.weierstrass_coeffs Weierstrass equation or model
hgm.weight weight
mf.slash_action Weight $k$ slash-action
mf.hilbert.weight_vector Weight of a Hilbert modular form
st_group.weight Weight of a Sato-Tate group
nf.weil_height Weil height
av.fq.weil_polynomial Weil q-polynomial
ag.weil_chatelet Weil-Châtelet group
group.fuchsian.cusps.width Width of a cusp
mot.width Width of a motive
lf.wild_inertia_group Wild inertia group
group.wreath_product Wreath product
Z
lfunction.zfunction Z-function of an L-function
group.z_group Z-group
ring.zero_divisor Zero divisor
lfunction.zeros Zeros of an L-function
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content.news
curve.highergenus.aut.sort_order
mf.bianchi.fourierbessell
mf.bianchi.weight2
sage.cell
users.kedlaya.note
users.lewismcombes.note
users.pascal.note
g2c.gl2type $\GL_2$-type
ec.q_curve $\mathbb{Q}$-curves
specialfunction.k_bessel $K$-Bessel functions
lf.padic_field $p$-adic field
g2c.two_selmer_rank 2-Selmer rank
g2c.two_torsion_field 2-torsion field