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A
ag.abelian_surface Abelian surface
ag.abelian_variety Abelian variety
group.galois.absolute Absolute Galois group
ag.curve Algebraic curve
ag.variety Algebraic variety
ec.q.analytic_sha_order Analytic order of Ш
artin.lfunction Artin L-function
nf.assuming_grh Assuming GRH
mf.elliptic.atkinlehner Atkin-Lehner eigenvalue
mf.maass.mwf.atkinlehner Atkin-Lehner eigenvalues
bio.selberg Atle Selberg
B
mf.bianchi.bianchigroup Bianchi Groups
mf.bianchi.bianchimodularforms Bianchi modular forms
ec.q.galois_rep_image_borel Borel case
C
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
gg.character_table.data Character table data
ec.complex_multiplication Complex Multiplication
character.dirichlet.conductor Conductor of a Dirichlet character
data.congruent_numbers Congruent numbers data
gg.conjugacy_classes.data Conjugacy class representatives
gg.conjugacy_classes Conjugacy classes
riemann.stieltjes.contents Contents of our Stieltjes constants tables
doc.create_knowl Create a knowl
doc.create_account Create an account
ec.q.cremona_label Cremona label
lfunction.critical_line Critical line of an L-function
lfunction.critical_strip Critical strip
crystals.crystal Crystals
mf.elliptic.cusp_form Cusp form (elliptic)
D
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
lfunction.degree 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
character.dirichlet.group Dirichlet character group
lfunction.dirichlet Dirichlet L-function
lfunction.dirichlet_series Dirichlet series
lf.discriminant_exponent Discriminant exponent of a local field
lf.discriminant_root_field Discriminant root field of a local field
mf.siegel.lift.ikeda Duke-Imamoglu-Ikeda lift
E
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
ec.q.endomorphism_ring Endomorphism Ring
mf.11.2.0.a.formulas eta-product
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
ec.q.galois_rep_image_exc Exceptional case
doc.view_knowl Expand a knowl
F
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
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
G
gg.galois_group Galois group
nf.galois_group.data 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
ec.q.galois_rep Galois representation
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
mf.siegel.lift.gritsenko Gritsenko lift
gg.group_action_invariants Group action Invariants
gg.invariants Group invariants
H
mf.half_integral_weight Half-integral weight modular forms
bio.harald_schilly Harald Schilly
mf.elliptic.hecke-orbit Hecke orbit
hgm.field.label HGM Labels
crystals.highest_weight Highest weight crystals
content.how-to-cite How to cite LMFDB
mf.upper-half-plane Hyperbolic 2-space
mf.bianchi.hyperbolic3space Hyperbolic 3-space
I
doc.knowl.identifier Identifier of a knowl
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
ec.q.integral_points Integral points
nf.intermediate_fields Intermediate fields
intro Introduction
intro.features Introduction/Features
intro.tutorial Introduction/Tutorial
J
ec.q.j_invariant j-invariant
af.jacobi Jacobi forms
character.dirichlet.jacobi_sum Jacobi sum
K
character.dirichlet.kloosterman_sum Kloosterman sum
dirichlet_character.kloosterman_sum Kloosterman sum
doc.knowl Knowl
test.knowlparam Knowl with parameters
ec.q.kodaira_symbol Kodaira symbol
character.dirichlet.kronecker_symbol Kronecker symbol
L
lfunction.definition L-function
lfunction.spectral_parameters L-function spectral parameters
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
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
M
mf.maass.mwf Maass form on GL2(R)
mf.maass.picard Maass forms on PSL(2,Z[i])
uploader.mapping_rules Mapping rules
mf.elliptic.minimal Minimal modular form
ec.q.minimal_weierstrass_equation Minimal Weierstrass equation over $\mathbb Q$
demo.aim.mission_statement Mission statement of AIM
mf.siegel.lift.miyawaki Miyawaki lift
character.dirichlet.modulus Modulus of a Dirichlet character
ec.mordell_weil Mordell-Weil group
nf.multiplicative_gal_module Multiplicative Galois Module Structure
mf.maass.mwf.dimension Multiplicity of an eigenvalue
N
doc.knowl.naming_conventions Naming conventions for knowls
doc.knowl.naming_suggestions Naming suggestions
mf.elliptic.newform Newform
ec.q.non-surjective_prime Non-surjective prime
ec.q.galois_rep_image_nsp_cartan nonsplit Cartan case
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
O
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
mf.siegel.group.paramodular 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
character.dirichlet.primitive Primitive Dirichlet character
character.dirichlet.basic_properties Properties of Dirichlet characters
Q
mf.elliptic.q-expansion q-expansion of an elliptic modular form
mf.hilbert.q_expansion q-expansion of Hilbert Cusp Form
R
character.dirichlet.real Real Dirichlet character
ec.q.real_period Real period
lfunction.riemann Riemann zeta-function
dirichlet_character.roadmap Roadmap for Dirichlet characters
lfunction.roadmap Roadmap for L-functions
mf.maass.roadmap Roadmap for Maass forms
S
sage.cellexample Sage cell example
sage.test Sage cell knowl
mf.siegel.lift.saito_kurokawa Saito-Kurokawa lift
ec.q.21168.ce2.top secp256k1 elliptic curve
lfunction.selberg_class.axioms Selberg class axioms
lfunction.selberg_class Selberg class of L-functions
nf.separable Separable extension
doc.lmfdb.share Sharing goal of the LMFDB
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
mf.siegel.halfspace Siegel upper half space
lfunction.root_number Sign of an L-function
lfunction.signature Signature of an L-function
lfunction.special_values Special values of an L-function
ec.q.galois_rep_image_sp_cartan split Cartan case
riemann.stieltjes_constants Stieltjes constants
mf.sturm_bound Sturm bound
gg.subfields Subfields
ec.q.surjective_prime Surjective prime
mf.siegel.group.symplectic Symplectic group
T
zeros.first.contents Table of first zeros of L-function
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
ec.field.torsion_order Torsion order of an elliptic curve
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
U
lfunction.underlying_object Underlying object of an L-function
doc.upload_data Upload data
V
lfunction.value Value of an L-function
character.dirichlet.values Values of a Dirichlet character
mf.siegel.vector_valued Vector-valued Siegel modular forms
W
ec.weierstrass_coeffs Weierstrass equation/coefficients
mf.hilbert.weight_vector Weight of a Hilbert modular form
mot.width Width of a motive
bio.william_stein William Stein
Z
lfunction.zfunction Z-function of an L-function
lfunction.zeros Zeros of an L-function
?
mf.1-12-0-a.formulas
mf.elliptic.coefficient_field
lfunction.riemann.bottom
mf.maass.mwf.plot
mf.2.8.0.a.formulas
mf.3.6.0.a.formulas
mf.4.5.1.a.formulas
mf.4.6.0.a.formulas
mf.5.4.0.a.formulas
mf.6.4.0.a.formulas
mf.7.3.3.a.formulas
mf.elliptic.explicit_formula
sage.cell
users.pascal.note
mf.half_integer_weight
doc.related_to "related to" field