A Serre derivative for even weight Jacobi Forms

Georg Oberdieck

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arXiv · 1209.5628

A Serre derivative for even weight Jacobi Forms

Georg Oberdieck

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Abstract

Using deformed or twisted Eisenstein Series, we construct a Jacobi-Serre derivative on even-weight Jacobi forms that generalizes the classical Serre derivative on modular forms. As an application, we obtain Ramanujan equations for the index $1$ Eisenstein series $E_{4,1}, E_{6,1}$ and a newly defined $E_{2,1}$. Finally, we relate the deformed Eisenstein Series directly to the classical first Jacobi theta function.

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Georg Oberdieck. 2014-06-11. A Serre derivative for even weight Jacobi Forms. https://arxiv.org/abs/1209.5628

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