- ID: DavidFarmer

## Knowls

David Farmer has contributed to these Knowls:
A history of L-functions,
A tour of the Riemann zeta function,
Acknowledgments for Maass forms,
Action of $\SL(2,\R)$ in the upper half-plane,
Algebraic variety ,
Analytic conductor of a classical newform,
Analytic order of Ш,
Analytic rank,
Arithmetic L-function,
Artin L-functions,
Artin representation (definition),
Atkin-Lehner involution $w_Q$,
Available samples for $M_k(\mathrm{Sp}(4,\mathbb{Z}))$,
Bad prime,
Basic properties of Dirichlet characters,
Bernoulli numbers,
Birch and Swinnerton-Dyer conjecture,
Birch and Swinnerton-Dyer invariants of an elliptic curve/$\mathbb{Q}$,
CM form,
Central point of an L-function,
Central value of an L-function,
Character of a Maass form,
Character of a modular form,
Class number of a number field,
Completed L-function,
Completeness and extent of Maass form data,
Conductor of a Dirichlet character,
Conductor of an elliptic curve,
Conductor of an elliptic curve over $\Q$,
Containing permutation representation,
Critical line of an L-function,
Critical strip,
Cusps of a subgroup of the modular group,
Dedekind zeta-functions, history,
Defining Polynomial of a Number Field,
Defining polynomial,
Degree 1 L-functions, all,
Degree 2 L-functions, examples,
Degree 3 L-functions, examples,
Degree 4 L-functions, examples,
Degree of a local field extension,
Degree of a number field,
Degree of an L-function,
Density of an integral lattice,
Developers Guide,
Dimension,
Dimension of an algebraic variety,
Dimensions of Atkin-Lehner subspaces,
Dirichlet character,
Dirichlet series,
Dirichlet's work on L-functions,
Duke-Imamoglu-Ikeda lift,
Elliptic curve invariants,
Elliptic curve over a field,
Euler gamma function,
Euler product of an L-function,
Euler's work on the zeta function,
Fourier coefficients of a modular form,
Fourier expansion of Maass form,
Fricke involution,
Functional equation of an L-function,
Fundamental domain,
Fundamental units of a number field,
Galois group of a number field -- naming convention,
Galois orbit of a Dirichlet character,
Galois orbit of a newform,
Gauss sum,
Hecke L-functions,
Hecke operator,
Hecke operators, history,
Hecke orbit,
Holomorphic Eisenstein series of level 1,
How to cite the LMFDB,
Ideal class group of a number field,
Index page, first sentences,
Introduction,
Introduction/Features,
Isogeny graph legend,
Jacobi forms,
Knowl,
L-function,
L-function of a classical modular form,
L-functions of Maass forms,
LMFDB Press,
LMFDB backend,
LaTeX macros in the LMFDB,
Label of a classical modular form,
Laplace-Beltrami operator (hyperbolic),
Level of a modular form,
Local data of an elliptic curve,
Maass form coefficients,
Maass form on GL2(R) with trivial character,
Maass lift from Jacobi form to Siegel modular form,
Management board,
Minimal modular form,
Minimal polynomial,
Miyawaki lift ,
Modular form (general),
Modular form associated to an elliptic curve/$\mathbb Q$,
Modular group $\mathrm {SL}(2,\mathbb Z)$,
Motivic weight,
Naming suggestions,
Newform,
Nk^2,
Normalization of an L-function,
Normalization of defining polynomials for number fields,
Number field label,
Number field nicknames,
Optimal elliptic curve over $\mathbb Q$,
Petersson scalar product,
Primitive L-function,
Ramanujan tau L-function,
Ranking-Selberg convolution, history,
Rational L-function,
Real multiplication,
Reliability of Elliptic Curve L-function Data,
Reliability of Maass forms data,
Riemann zeta-function,
Riemann's memoir,
Roadmap for Hilbert modular forms,
Roadmap for L-functions,
Roadmap for Maass forms,
Roadmap for elliptic curves,
Roadmap for future areas of LMFBD,
Roadmap for local number fields,
Root number of an Artin representation,
Sato-Tate group of a genus 2 curve over Q,
Selberg class of L-functions,
Selberg data for the functional equation of an L-function,
Siegel modular form Hecke operators,
Siegel modular forms, history,
Siegel theta series and theta series with pluriharmonics,
Sign of an L-function,
Sign of the functional equation,
Signature of an L-function,
Source of Maass forms data,
Source of elliptic curve data over $\Q$,
Space of newforms,
Spaces of modular forms,
Special value of an elliptic curve L-function,
Subgroup $\Gamma(N)$ of $\textrm{SL}(2,\mathbb{Z})$,
Subgroup $\Gamma_0(N)$ of $\textrm{SL}(2,\mathbb{Z})$,
Subgroup $\Gamma_1(N)$ of $\textrm{SL}(2,\mathbb{Z})$,
Subspaces of modular forms,
Tate's thesis,
Taxonomy of L-functions,
The eigenvalue of a Maass form,
The level of a Maass form,
The symmetry of a Maass form,
Theta constant,
Torsion order of an elliptic curve,
Trace bound,
Transformation property for modular forms,
Trivial zeros of an L-function,
Underlying object of an L-function,
Unit group of a number field,
Unramified (rational) prime of a number field,
Upper half-plane,
Values of a Dirichlet character,
Vector-valued Siegel modular forms,
Weight of an elliptic modular form,
Weil height,
Width of a cusp,
Z-function of an L-function,
Zeros of an L-function,
q-expansion of a modular form