Period Relations, Jacobi Forms and Eichler Integral

TL;DR

This paper investigates the period relations of Jacobi forms, showing that relations from Mordell integrals are special cases, and discusses the existence of Jacobi integrals linked to period functions via generalized Poincaré series.

Contribution

It introduces a framework connecting period relations of Jacobi forms with Mordell integrals and establishes the existence of Jacobi integrals through generalized Poincaré series.

Findings

Relations from Mordell integrals are special cases of Jacobi form period relations

Existence of Jacobi integrals associated with period functions is demonstrated

Provides a new perspective on the structure of Jacobi forms and their integrals

Abstract

We study period relations of Jacobi forms. It turns out that the relations satisfied by Mordell integral coming from Lerch or Appell sums are the special case of those. The existence of Jacobi integral associated to given period function using generalized Poincar\'e series is claimed.