Search Filter Category: af ag artin bio character content data demo dirichlet_character doc ec gg group intro lf lfunction mf mwf nf sage specialfunction test uploader zeros crystals Quality: Beta Ok Reviewed More Recently modified Knowls
 A group.galois.absolute Absolute Galois group ag.curve Algebraic curve ag.curve.genus Algebraic genus of a smooth curve ag.variety Algebraic variety lfunction Analytic L-function 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 lf.automorphism_group Automorphism group of a field extension B ec.q.bsdconjecture Birch and Swinnerton-Dyer conjecture ec.q.bsd_invariants Birch and Swinnerton-Dyer invariants of an elliptic curve/$\mathbb{Q}$ 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 nf.class_number Class number of a number field ec.complex_multiplication Complex Multiplication character.dirichlet.conductor Conductor of a Dirichlet character artin.conductor Conductor of an Artin representation ec.q.conductor Conductor of an elliptic curve over $\mathbb{Q}$ data.congruent_numbers Congruent numbers data gg.conjugacy_classes.data Conjugacy class representatives gg.conjugacy_classes Conjugacy classes artin.database_comment Content of the Artin representations database 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) mf.sl2z.subgroup.cusps Cusps of a subgroup of the modular group D zeros.zeta.contents David Platt's computation of zeros of the zeta function 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 lf.degree Degree of a local field extension nf.degree Degree of a number field lfunction.degree Degree of an L-function doc.knowl.description Description field in knowls mf.hilbert.dimension Dimension of a Hecke constituent artin.dimension Dimension of an Artin representation mwf.dimension Dimension of an eigenvalue bio.dirichlet Dirichlet (biography) 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 nf.discriminant Discriminant of a number field ec.q.discriminant Discriminant of an elliptic curve over $\mathbb Q$ 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 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.fricke Fricke eigenvalue nf.frobenius_cycle_types Frobenius cycle types artin.frobenius_schur_indicator Frobenius-Schur indicator of the representation lfunction.functional_equation Functional equation of an L-function nf.fundamental_units Fundamental units of a number field G gg.galois_group Galois group nf.galois_group.data Galois group information gg.label Galois group label nf.galois_group Galois group of a number field nf.galois_group.name Galois group of a number field -- naming convention lf.galois_invariants Galois invariants of a local field mf.siegel.galois_orbit Galois orbit character.dirichlet.galois_orbit Galois orbit of a Dirichlet character character.dirichlet.gauss_sum Gauss sum lfunction.rh Generalized Riemann hypothesis nf.field_generator Generator of a number field character.dirichlet.values_on_gens Generators of the group of Dirichlet characters mf.sl2z.subgroup.genus Genus of a subgroup of the modular group bio.riemann Georg Friedrich Bernhard Riemann demo.knowl.grants Grants supporting the development of knowls mf.siegel.lift.gritsenko Gritsenko lift mf.sl2.subgroup.gamma0N Group $\Gamma_0(N)$ subgroup of $\mathrm{SL}(2,\mathbb Z)$ mf.sl2.subgroup.gamma0n Group $\Gamma_0(N)$ subgroup of $\textrm{SL}(2,\mathbb{Z})$ mf.siegel.group.gamma0 Group $\Gamma_0(N)$, subgroup of $\mathrm{Sp}(2g,\mathbb Z)$ mf.sl2.subgroup.gamma1n Group $\Gamma_1(N)$ subgroup of $\textrm{SL}(2,\mathbb{Z})$ gg.group_action_invariants Group action Invariants gg.invariants Group invariants mf.growth_condition Growth condition for a modular form H bio.harald_schilly Harald Schilly crystals.highest_weight Highest weight crystals mf.hilbert Hilbert modular form ec.q.5077a1.top Historical information for 5077a1 mf.elliptic Holomorphic modular form (elliptic) I nf.ideal_class_group Ideal class group of a number field doc.knowl.identifier Identifier of a knowl artin.gg_quotient Image of the representation doc.knowl.implicit Implicit creation of knowls mf.sl2z.subgroup.index Index of a subgroup of the modular group intro.description Index page, first sentences nf.integral_basis Integral basis of a number field ec.q.integral_points Integral points intro Introduction intro.features Introduction/Features intro.tutorial Introduction/Tutorial ec.isogeny_class Isogeny class of an elliptic curve ec.isogeny Isogeny of elliptic curves J ec.q.j_invariant j-invariant af.jacobi Jacobi forms character.dirichlet.jacobi_sum Jacobi sum K dirichlet_character.kloosterman_sum Kloosterman sum character.dirichlet.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 ec.q.lmfdb_label Label for an elliptic curve over $\mathbb Q$ mf.elliptic.label Label of a holomorphic cusp form on GL(2) mf.maass.mwf.laplacian Laplace-Beltrami operator (hyperbolic) mf.maass.picard.laplacian Laplacian in 3d hyperbolic upper half-space 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 Maass forms on GL(n) mf.maass.picard Maass forms on PSL(2,Z[i]) mf.siegel.lift.maass Maass lift from Jacobi form to Siegel modular form 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 ec.q.modular_degree Modular degree of an elliptic curve over $\mathbb Q$ ec.q.modular_form Modular form associated to an elliptic curve/$\mathbb Q$ ec.q.modular_parametrization Modular parametrization of an elliptic curve over $\mathbb Q$ character.dirichlet.modulus Modulus of a Dirichlet character ec.mordell_weil Mordell-Weil group ec.q.mordell-weil Mordell-Weil group of an elliptic curve over a number field 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 ag.singular_point Non-singular point (definition) nf.defining_polynomial.normalization Normalization of defining polynomials for number fields artin.number_field Number field associated to an Artin representation nf.invariants Number field invariants nf.label Number field label nf.nickname Number field nicknames character.dirichlet.related_fields Number fields related to a Dirichlet character O demo.grassy_knoll obsolete ec.q.optimal Optimal elliptic curve over $\mathbb Q$ 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 R lf.ramification_index Ramification index of a prime in a local field nf.ramified_primes Ramified (rational) prime of a number field nf.ramified_prime Ramified prime of a number field nf.rank Rank of a number field character.dirichlet.real Real Dirichlet character ec.q.real_period Real period ec.q.reduction_type Reduction type of an elliptic curve over $\mathbb Q$ nf.regulator Regulator of a number field ec.q.regulator Regulator of elliptic curve lf.residue_field_degree Residue field degree of an extension of local fields lfunction.riemann Riemann zeta-function nf.ring_of_integers Ring of integers of a number field artin.roadmap Roadmap for Artin representations dirichlet_character.roadmap Roadmap for Dirichlet characters ec.roadmap Roadmap for elliptic curves mf.elliptic.roadmap Roadmap for elliptic modular forms content.roadmap Roadmap for future areas of LMFBD gg.roadmap Roadmap for Galois groups mf.hilbert.roadmap Roadmap for Hilbert modular forms lfunction.roadmap Roadmap for L-functions lf.roadmap Roadmap for local number fields mf.maass.roadmap Roadmap for Maass forms nf.roadmap Roadmap for number fields mf.siegel.roadmap Roadmap for Siegel modular forms nf.root_discriminant Root discriminant of a number field lf.root_number Root number of a local field artin.root_number Root number of an Artin representation S sage.test Sage cell knowl mf.siegel.lift.saito_kurokawa Saito-Kurokawa lift lfunction.selberg_class.axioms Selberg class axioms lfunction.selberg_class Selberg class of L-functions lfunction.selbergdata Selberg data for the functional equation of an L-function nf.separable Separable extension doc.lmfdb.share Sharing goal of the LMFDB 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 Siegel modular form mf.siegel.hecke_operator Siegel modular form Hecke operators mf.siegel.character Siegel modular form with character mf.siegel.theta_series Siegel theta series and theta series with pluriharmonics mf.siegel.halfspace Siegel upper half space lfunction.root_number Sign of an L-function lfunction.sign Sign of the functional equation nf.signature Signature of a number field lfunction.signature Signature of an L-function ag.curve.smooth Smooth algebraic curve (definition) ec.q.special_value Special value of an elliptic curve L-function lfunction.special_values Special values of an L-function mf.maass.picard.eigenvalue Spectral parameter of Maass forms on PSL(2,Z[i]) gg.subfields Subfields lfunction.symm Symmetric power of an L-function mf.siegel.group.symplectic Symplectic group T gg.tnumber T-number of a transitive group zeros.first.contents Table of first zeros of L-function ec.q.tamagawa_numbers Tamagawa numbers for an elliptic curve 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.q.torsion_generators Torsion generators of an elliptic curve over $\mathbb Q$ ec.torsion_order Torsion order of an elliptic curve ec.field.torsion_order Torsion order of an elliptic curve ec.q.torsion_order Torsion order of an elliptic curve over $\mathbb{Q}$ ec.torsion_subgroup Torsion subgroup of an elliptic curve ec.q.torsion_subgroup Torsion subgroup of an elliptic curve over $\mathbb Q$ nf.totally_positive totally positive nf.totally_real Totally real doc.knowl.context_free Transclusion (definition) mf.transformation_property Transformation property for modular forms U lfunction.underlying_object Underlying object of an L-function nf.unit_group Unit group of a number field nf.unramified_prime Unramified (rational) prime of a number field 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 mf.elliptic.weight Weight of an elliptic modular form doc.wiki Wiki (definition) bio.william_stein William Stein Z lfunction.zfunction Z-function of an L-function lfunction.zeros Zeros of an L-function ? mf.3.6.0.a.formulas mf.7.3.3.a.formulas mf.elliptic.explicit_formula mf.4.6.0.a.formulas mf.1-12-0-a.formulas lfunction.riemann.bottom mf.2.8.0.a.formulas mf.4.5.1.a.formulas mf.5.4.0.a.formulas mf.6.4.0.a.formulas lfunction.taxonomy doc.related_to "related to" field specialfunction.gammarandc $\Gamma_{\mathbb R}$ and $\Gamma_{\mathbb C}$