English

Expansions at Cusps and Petersson Products in Pari/GP

Number Theory 2018-10-01 v1

Abstract

We begin by explaining how to compute Fourier expansions at all cusps of any modular form of integral or half-integral weight thanks to a theorem of Borisov-Gunnells and explicit expansions of Eisenstein series at all cusps. Using this, we then give a number of methods for computing arbitrary Petersson products. All this is available in the current release of the Pari/GP package.

Keywords

Cite

@article{arxiv.1809.10908,
  title  = {Expansions at Cusps and Petersson Products in Pari/GP},
  author = {Henri Cohen},
  journal= {arXiv preprint arXiv:1809.10908},
  year   = {2018}
}