- ID: swisherh

## Knowls

Holly Swisher has contributed to these Knowls:
A tour of the Riemann zeta function,
Associative binary operation,
Bianchi modular forms,
Character of a modular form,
Class number of a number field,
Classical modular form,
Commutative binary operation,
Complex embedding,
Congruence subgroup of a Bianchi group,
Cuspidal modular form,
Defining Polynomial of a Number Field,
Definition of ring,
Degree 1 L-functions, all,
Degree 2 L-functions, examples,
Degree 3 L-functions, examples,
Degree 4 L-functions, examples,
Degree of a number field,
Degree of an L-function,
Dirichlet L-function,
Discriminant of a number field,
Euler gamma function,
Field,
Fourier-Bessel expansion,
Fractional ideal,
Functional equation of an L-function,
Fundamental units of a number field,
Galois group,
Galois orbit,
Gamma factors,
Generator of a number field,
Growth condition for a modular form,
Hecke character,
Hecke orbit for Hilbert modular form,
Hilbert modular form,
Hilbert modular form convention for the label of a number field ideal,
Ideal class group of a number field,
Identity for a binary operation,
Integral basis of a number field,
Introduction,
Introduction/Features,
Inverse for a binary operation,
Kloosterman sum,
L-function,
Laplace-Beltrami operator (hyperbolic),
Laplacian in 3d hyperbolic upper half-space,
Level of a Bianchi modular form,
Level of a Hilbert modular form,
Level of a modular form,
Maass form on GL2(R) with trivial character,
Maass forms on GL(n),
Maass forms on PSL(2,Z[i]),
Minimal Weierstrass equation over $\mathbb Q$,
Minimal modular form,
Modular form (general),
Newform,
Number field,
Number field invariants,
Number field label,
Primitive L-function,
Ramified (rational) prime of a number field,
Rank of a number field,
Real embedding,
Regulator of a number field,
Roadmap for L-functions,
Sage Mathematical Software System,
Sage cell knowl,
Selberg class axioms,
Selberg data for the functional equation of an L-function,
Siegel modular form,
Sign of an L-function,
Signature of a number field,
Special value of an elliptic curve L-function,
The spectral parameter of a Maass waveform,
Transformation property for modular forms,
Underlying object of an L-function,
Unit group of a number field,
Unramified (rational) prime of a number field,
Values of a Dirichlet character on generators,
Weight 2 Bianchi modular forms,
Weight of a Bianchi modular form,
Weight of an elliptic modular form,
q-expansion of a Hilbert modular form,
q-expansion of a modular form