Computing genus 1 Jacobi forms

Raum, Martin

doi:10.1090/mcom/2992

Computing genus $1$ Jacobi forms
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Math. Comp. 85 (2016), 931-960 Request permission

Abstract:

We develop an algorithm to compute Fourier expansions of vector valued modular forms 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.

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