A Serre derivative for even weight Jacobi Forms

2012/09/25 by Georg Oberdieck, Oberdieck, Georg
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1209.5628

12 pages. New version

openalex publication_date 2012/09/25 · arxiv created 2014/06/11 · arxiv updated 2014/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• Harmonic Maass-Jacobi forms with singularities and a theta-like decomposition

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