A Serre derivative for even weight Jacobi Forms

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.

12 pages. New version

References in corpus (1)

• Quantum Black Holes, Wall Crossing, and Mock Modular Forms

Cited by in corpus (4)

• Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition
• H-Harmonic Maass-Jacobi Forms of Degree 1: The Analytic Theory of Some Indefinite Theta Series
• Gauss-Manin connection in disguise: Quasi Jacobi forms of index zero
• Cohomology of Jacobi forms