Covariants of binary sextics and vector-valued Siegel modular forms of genus two

Fabien Cléry; Carel Faber; Gerard van der Geer

Covariants of binary sextics and vector-valued Siegel modular forms of genus two

Algebraic Geometry 2019-08-14 v1 Number Theory

Authors: Fabien Cléry , Carel Faber , Gerard van der Geer

Abstract

We extend Igusa's description of the relation between invariants of binary sextics and Siegel modular forms of degree two to a relation between covariants and vector-valued Siegel modular forms of degree two. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree two.

Keywords

binary sextics covariants vector-valued Siegel modular forms genus two Fourier expansions Igusa invariants

Cite

@article{arxiv.1606.07014,
  title  = {Covariants of binary sextics and vector-valued Siegel modular forms of genus two},
  author = {Fabien Cléry and Carel Faber and Gerard van der Geer},
  journal= {arXiv preprint arXiv:1606.07014},
  year   = {2019}
}