On congruences of Jacobi forms

Richter, Olav

doi:10.1090/S0002-9939-08-09274-5

On congruences of Jacobi forms
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by Olav K. Richter

Proc. Amer. Math. Soc. 136 (2008), 2729-2734

DOI: https://doi.org/10.1090/S0002-9939-08-09274-5

Published electronically: April 15, 2008

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Abstract:

We consider congruences and filtrations of Jacobi forms. More specifically, we extend Tate’s theory of theta cycles to Jacobi forms, which allows us to prove a criterion for an analog of Atkin’s $U$-operator applied to a Jacobi form to be nonzero modulo a prime.

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