Computing Genus 1 Jacobi Forms

2012/12/08 by Martin Raum, Raum, Martin
Mathematics · #11F27 #11G18 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Primary: 11F30 #Secondary: 11F50 #math.AG #math.NT #msc:11F27 #msc:11F30 #msc:11F50 #msc:11G18

paper · pdf · doi:10.48550/arxiv.1212.1834

31 pages, code available via github, additional data available at the author's webpage

arxiv created 2014/09/18 · arxiv updated 2014/09/19

Abstract

We develop an algorithm to compute Fourier expansions of vector valued modular for Weil representations. As an application, we compute explicit linear equivalences of special divisors on modular varieties of orthogonal type. We define three families of Hecke operators for Jacobi forms, and analyze the induced action on vector valued modular forms. The newspaces attached to one of these families are used to give a more memory efficient version of our algorithm.

Related

• On the Computation of General Vector-valued Modular Forms
• The Weil representation and Hecke operators for vector valued modular forms
• Jacobi Forms of Critical Weight and Weil Representations
• Jacobi Forms of Degree One and Weil Representations
• Pointwise Properties of Fourier-Jacobi-Forms