Computing Jacobi Forms
Number Theory
2019-02-20 v2
Abstract
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.
Keywords
Cite
@article{arxiv.1602.07021,
title = {Computing Jacobi Forms},
author = {Nathan C. Ryan and Nicolás Sirolli and Nils-Peter Skoruppa and Gonzalo Tornaría},
journal= {arXiv preprint arXiv:1602.07021},
year = {2019}
}
Comments
14 pages, 5 tables, Cython implementation of algorithm included. Revised version. To appear in the LMS Journal of Computation and Mathematics