Contents

  1. Definitions
    1. Congruence subgroups
    2. Weights
    3. Definition of Siegel modular forms
  2. Fourier expansions and Fourier-Jacobi expansions
  3. Cusp forms
  4. Dimension Formula
  5. Hecke theory
  6. $L$-functions
  7. Applications
    1. Arithmetic geometry
    2. Serre's conjecture for totally real number fields
  8. Computational Aspects
    1. Jacquet Langlands Correspondence
    2. Existing Databases
    3. Software (Magma file)
  9. References

Definitions

Congruence subgroups

Weights

Definition of Siegel modular forms

Fourier expansions and Fourier-Jacobi expansions

Cusp forms

Dimension Formula

Hecke theory

$L$-functions

Applications

Arithmetic geometry

Serre's conjecture for totally real number fields

Computational Aspects

Jacquet Langlands Correspondence

Existing Databases

Software (Magma file)

References

ModularForms/HilbertModularForms (last edited 2009-03-01 00:55:51 by localhost)