Filter Category: af ag artin bio character content crystals data demo dirichlet_character doc dq ec g2c gg group hgm intro lattice lf lfunction local_data mf mot mwf nf nf_weil_height riemann sage specialfunction test uploader users zeros varieties repn field
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lfunction.history A history of L-functions
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
ec.additive_reduction Additive reduction
nf.algebraic_closure Algebraic closure of a field
ag.curve Algebraic curve
ag.variety Algebraic variety
ec.q.analytic_sha_order Analytic order of Ш
ec.q.analytic_sha_value Analytic order of Sha (numerical value)
lfunction.arithmetic Arithmetic L-function
artin.lfunction Artin L-function
lfunction.history.artin Artin L-functions
nf.assuming_grh Assuming GRH
mf.elliptic.atkinlehner Atkin-Lehner eigenvalue
mf.maass.mwf.atkinlehner Atkin-Lehner eigenvalues
mf.elliptic.atkin-lehner Atkin-Lehner operator $W_Q$ on $X_0(N)$
bio.selberg Atle Selberg
ec.base_change Base change
mf.bianchi.bianchigroup Bianchi Groups
mf.bianchi.bianchimodularforms Bianchi modular forms
ec.q.galois_rep_image_borel Borel case
ec.q.canonical_height Canonical height
lattice.catalogue_of_lattices Catalogue of Lattices
lfunction.central_character Central character of an L-function
lfunction.central_value Central value of an L-function
mf.maass.mwf.character Character of a Maass form
mf.elliptic.character Character of a modular form Character table data
ag.cm_field CM field
mf.elliptic.cm_form CM form
ec.complex_multiplication Complex multiplication
ag.complex_multiplication Complex multiplication
character.dirichlet.conductor Conductor of a Dirichlet character
lfunction.conductor Conductor of an L-function
ec.conductor_valuation Conductor valuation
data.congruent_numbers Congruent numbers data Conjugacy class representatives
gg.conjugacy_classes Conjugacy classes
artin.permutation_container Containing permutation representation
riemann.stieltjes.contents Contents of our Stieltjes constants tables
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
mf.elliptic.cusp_form Cusp form (elliptic)
lfunction.history.dedekind Dedekind zeta-functions, history
lf.defining_polynomial Defining polynomial of a local field
nf.defining_polynomial Defining Polynomial of a Number Field 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 Degree of an L-function
doc.knowl.description Description field in knowls
doc.development Developers Guide
mf.hilbert.dimension Dimension of a Hecke constituent
mf.elliptic.dimension_galois_orbit Dimension of a Hecke orbit
mf.elliptic.hecke-orbit-dimension Dimension of a Hecke orbit
character.dirichlet Dirichlet character 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 Discriminant modular form
lf.discriminant_root_field Discriminant root field of a local field
ec.discriminant_valuation Discriminant valuation
lattice.dual Dual lattice
mf.siegel.lift.ikeda Duke-Imamoglu-Ikeda lift
E E_8 Lattice
local_data ec.local_data
content.edit-board Editorial board and management
ec.q.37.a1.bottom Elliptic Curve 37a1
ec.q.invariants Elliptic curve invariants
bio.artin Emil Artin
ag.endomorphism_algebra Endomorphism algebra
g2c.jac_endomorphisms Endomorphism invariants
ec.q.endomorphism_ring Endomorphism ring
ag.endomorphism_ring Endomorphism ring
ec.endomorphism_ring Endomorphism ring
mf.4.6.0.a.formulas eta function product formula
mf.11.2.0.a.formulas eta-product
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
ec.q.galois_rep_image_exc Exceptional case
doc.view_knowl Expand a knowl
dq.zeros.zeta.extent Extent of Riemann zeta zeros data
nf.20.2.206007596521214410095208558252435839890349094339.1.bottom Field associated with 19-torsion on an elliptic curve
character.dirichlet.field_cut_out Field cut out by a Dirichlet character
character.dirichlet.field_values Field of values
mf.1.12.0.a.formulas Formulas for Delta(z)
mf.maass.picard.fourierexpansion Fourier expansion of a Maass form on PSL(2,Z[i])
mf.maass.mwf.fourierexpansion Fourier expansion of Maass form
mf.maass.mwf.fricke Fricke eigenvalue
mf.elliptic.fricke Fricke involution for Gamma_0
nf.frobenius_cycle_types Frobenius cycle types
artin.frobenius_schur_indicator Frobenius-Schur indicator of a representation
lfunction.functional_equation Functional equation of an L-function
gg.galois_group Galois group Galois group information
lf.galois_invariants Galois invariants of a local field
nf.galois_group.gmodule Galois module information
mf.elliptic.galois-orbits Galois orbit
mf.siegel.galois_orbit Galois orbit
character.dirichlet.galois_orbit Galois orbit of a Dirichlet character
character.dirichlet.gauss_sum Gauss sum
nf.field_generator Generator of a number field
character.dirichlet.values_on_gens Generators of the group of Dirichlet characters
g2c.g2curve Genus 2 curve
ag.curve.genus Genus of a smooth curve
g2c.geom_aut_grp Geometric automorphism group
ag.geom_simple Geometrically simple
ec.global_minimal_model Global minimal model
ec.good_reduction Good reduction
lattice.gram Gram matrix
mf.siegel.lift.gritsenko Gritsenko lift
gg.group_action_invariants Group action Invariants
gg.invariants Group invariants
mf.half_integral_weight Half-integral weight modular forms
bio.harald_schilly Harald Schilly
nf.17.1.604462909807314587353088.1.bottom Harbater number field
lfunction.history.hecke_characters Hecke L-functions
lfunction.history.hecke_operators Hecke operators, history
mf.elliptic.hecke-orbit Hecke orbit
lattice.hermite_number Hermite number
hgm.field.label HGM Labels
crystals.highest_weight Highest weight crystals How to cite the LMFDB
mf.upper-half-plane Hyperbolic 2-space
mf.bianchi.hyperbolic3space Hyperbolic 3-space
ec.conductor_norm Ideal norm of conductor
doc.knowl.identifier Identifier of a knowl
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
intro.description Index page, first sentences
nf.integral Integral elements
lattice.definition Integral Lattice
ec.integral_model Integral model
ec.q.integral_points Integral points
nf.intermediate_fields Intermediate fields
intro Introduction
intro.features Introduction/Features
intro.tutorial Introduction/Tutorial
ec.weierstrass_isomorphism Isomorphism between Weierstrass models
ec.j_invariant_denominator_valuation j-invariant denominator valuation
af.jacobi Jacobi forms
character.dirichlet.jacobi_sum Jacobi sum
ag.jacobian Jacobian of a curve
lattice.kissing Kissing Number
character.dirichlet.kloosterman_sum Kloosterman sum
doc.knowl Knowl
doc.knowl.guidelines Knowl Edit Guidelines
test.knowlparam Knowl with parameters
ec.q.kodaira_symbol Kodaira symbol
ec.kodaira_symbol Kodaira symbol
character.dirichlet.kronecker_symbol Kronecker symbol
lfunction.definition L-function
lfunction.spectral_parameters L-function spectral parameters
lfunction.history.maass L-functions of Maass forms
mf.elliptic.character.label Label convention for Dirichlet characters
lf.field.label Label for a local field
lfunction.degree2holo.key Legend for GL(2) holomorphic graph of dots
character.dirichlet.legendre_symbol Legendre symbol
bio.euler Leonhard Euler
mf.hilbert.level_norm Level of a Hilbert modular form
mf.elliptic.level Level of a modular form
lfunction.level Level of an L-function
crystals.littelmann_path Littelmann path model for crystals
doc.lmfdb.improve LMFDB backend
lf.invariants Local field invariants
ec.local_minimal_discriminant Local minimal discriminant of an elliptic curve
ec.local_minimal_model Local minimal model
nf.14.2.79396891942519570432.1.bottom Low discriminant field
nf.14.2.536561726709678316933.1.bottom Low discriminant field
nf.17.1.239072435685151324847153.1.bottom Low discriminant field
nf.19.1.75613185918270483380568064.1.bottom Low discriminant field
mf.maass.mwf.browsegraph Maass form browsing graph explanation
mf.maass.mwf Maass form on GL2(R)
mf.maass.mwf.weight0 Maass forms of weight 0
mf.maass.picard Maass forms on PSL(2,Z[i])
uploader.mapping_rules Mapping rules
ec.minimal_discriminant Minimal discriminant
ec.minimal_discriminant_norm Minimal discriminant norm
mf.elliptic.minimal Minimal modular form
nf.minimal_polynomial Minimal polynomial
ec.q.minimal_weierstrass_equation Minimal Weierstrass equation over $\mathbb Q$
lattice.minimal_vector Minimum vector length
demo.aim.mission_statement Mission statement of AIM
mf.siegel.lift.miyawaki Miyawaki lift Modular curve $X_0(11)$ Modular curve $X_0(11)$
ag.modcurve.x0 Modular curve $X_0(N)$ Modular curve $X_1(11)$ Modular curve $X_1(11)$
ag.modcurve.x1 Modular curve $X_1(N)$
character.dirichlet.modulus Modulus of a Dirichlet character
ec.mordell_weil Mordell-Weil group
ec.mordell-weil Mordell-Weil theorem
nf.multiplicative_gal_module Multiplicative Galois Module Structure
ec.multiplicative_reduction Multiplicative reduction
mf.maass.mwf.dimension Multiplicity of an eigenvalue
N Name of a lattice
doc.knowl.naming_conventions Naming conventions for knowls
doc.knowl.naming_suggestions Naming suggestions
mf.elliptic.newform Newform
ec.q.galois_rep_image_nsp_cartan Non-split Cartan case
ec.nonsplit_multiplicative_reduction Non-split multiplicative reduction
ec.q.non-surjective_prime Non-surjective prime
nf.14.2.20325604337285010030592.1.bottom Nonsolvable field ramified at 2 and 13
nf.18.2.40254497110927943179349807054456171205137.1.bottom Nonsolvable field ramified at only 17
ec.discriminant_norm Norm of discriminant
nf.defining_polynomial.normalization Normalization of defining polynomials for number fields
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
demo.grassy_knoll obsolete
character.dirichlet.order Order of a Dirichlet character
group.order Order of a group
gg.other_representations Other representations of a group
P Paramodular group
mf.siegel.newform.paramodular Paramodular newform
character.dirichlet.parity Parity of a Dirichlet character
doc.lmfdb.contextualize Presentation of the data in the LMFDB
ag.bad_prime Prime of bad reduction
character.dirichlet.primitive Primitive Dirichlet character
lattice.primitive Primitive integral lattice
lfunction.primitive Primitive L-function
character.dirichlet.basic_properties Properties of Dirichlet characters
mf.hilbert.q_expansion q-expansion of a Hilbert modular form
mf.elliptic.q-expansion q-expansion of an elliptic modular form
lfunction.history.ramanujan_tau Ramanujan tau L-function
lfunction.history.rankin_selberg Ranking-Selberg convolution, history
character.dirichlet.real Real Dirichlet character
ag.real_endomorphism_algebra Real endomorphism algebra
ag.real_multiplication Real multiplication
ec.q.real_period Real period
ec.reduction_type Reduction type
lfunction.riemann Riemann zeta-function
lfunction.history.riemanns_memoir Riemann's memoir
dirichlet_character.roadmap Roadmap for Dirichlet characters
character.dirichlet.roadmap Roadmap for Dirichlet characters
lfunction.roadmap Roadmap for L-functions
mf.maass.roadmap Roadmap for Maass forms
ec.q.rouse-classification Rouse classification
ec.rouse_label Rouse label
sage.cellexample Sage cell example
sage.test Sage cell knowl
mf.siegel.lift.saito_kurokawa Saito-Kurokawa lift
ag.sato_tate_group Sato-Tate group (of a motive)
g2c.st_group_identity_component Sato-Tate group identity component secp256k1 elliptic curve
lfunction.selberg_class.axioms Selberg class axioms
lfunction.selberg_class Selberg class of L-functions
lfunction.self-dual Self-dual L-function
nf.separable Separable extension
mf.elliptic.shimura_correspondence Shimura correspondence
mf.half_integral_weight.shimura_decomposition Shimura decomposition
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
lfunction.root_number Sign of an L-function
lfunction.signature Signature of an L-function
ag.simple Simple
gg.simple_name Simple group name
nf.14.2.35632953415471973197.1.bottom Small discriminant field
lfunction.special_values Special values of an L-function
ec.q.galois_rep_image_sp_cartan Split Cartan case
ec.split_multiplicative_reduction Split multiplicative reduction
riemann.stieltjes_constants Stieltjes constants
mf.sturm_bound Sturm bound
gg.subfields Subfields
ec.q.surjective_prime Surjective prime Symplectic group
zeros.first.contents Table of first zeros of L-function
ec.tamagawa_number Tamagawa number
ec.padic_tate_module Tate module of an elliptic curve
lfunction.history.tates_thesis Tate's thesis
lfunction.taxonomy Taxonomy of L-functions
test.text Test → !!!
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
nf.18.2.4768875488962616064464333777.1.bottom Torsion field
g2c.torsion_order Torsion order
ec.field.torsion_order Torsion order of an elliptic curve
g2c.torsion Torsion subgroup
nf.totally_imaginary Totally imaginary
nf.totally_positive Totally positive
nf.totally_real Totally real
artin.trace_of_complex_conj Trace of complex conjugation
doc.knowl.context_free Transclusion (definition)
mf.transformation_property Transformation property for modular forms
lfunction.underlying_object Underlying object of an L-function
doc.upload_data Upload data
mf.upper_half_plane Upper half-pane
lfunction.value Value of an L-function
character.dirichlet.values Values of a Dirichlet character
mf.siegel.vector_valued Vector-valued Siegel modular forms
ec.weierstrass_coeffs Weierstrass equation or model
mf.hilbert.weight_vector Weight of a Hilbert modular form
nf_weil_height Weil height
mot.width Width of a motive
bio.william_stein William Stein
lfunction.zfunction Z-function of an L-function
lfunction.zeros Zeros of an L-function
doc.related_to "related to" field
g2c.gl2type $\GL_2$-type
nf.20.2.558854584859141340505879659895771.1.bottom 19-division field for CM elliptic curve for $\Q(\sqrt{-7})$
g2c.two_selmer_rank 2-Selmer rank 2450a1