Computing Jacobi Forms

Authors

Nathan C. Ryan, Bucknell UniversityFollow
Nicolás Sirolli, Universidad de Buenos Aires
Nils-Peter Skoruppa, Universität SiegenFollow
Gonzalo Tornaría, Universidad de la Republica, UruguayFollow

Publication Date

2016

Description

We describe an implementation for computing holomorphic and skew-holomorphic Jacobi forms of integral weight and scalar index on the full modular group. This implementation is based on formulas derived by one of the authors which express Jacobi forms in terms of modular symbols of elliptic modular forms. Since this method allows to generate a Jacobi eigenform directly from a given modular eigensymbol without reference to the whole ambient space of Jacobi forms it makes it possible to compute Jacobi Hecke eigenforms of large index. We illustrate our method with several examples.

Journal

London Mathematics Society Journal of Computational Mathematics

Volume

19

Issue

A

First Page

205

Last Page

219

Department

Mathematics

DOI

10.1112/S1461157016000346

Recommended Citation

Ryan, Nathan C.; Sirolli, Nicolás; Skoruppa, Nils-Peter; and Tornaría, Gonzalo. "Computing Jacobi Forms." London Mathematics Society Journal of Computational Mathematics (2016) : 205-219.