Construction of Jacobi forms using adjoint of the Jacobi–Serre derivative

Authors

Mrityunjoy Charan, Institute of Mathematical Sciences India
Lalit Vaishya, Institute of Mathematical Sciences India

Article Type

Research Article

Publication Title

Ramanujan Journal

Abstract

In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of the Oberdieck derivative of a Jacobi cusp form with respect to the Petersson scalar product defined on the space of Jacobi forms. As a consequence, we also obtain the adjoint of the Jacobi–Serre derivative (defined in an unpublished work of Oberdieck). As an application, we obtain certain relations among the Fourier coefficients of Jacobi forms.

First Page

189

Last Page

216

DOI

10.1007/s11139-024-00890-x

Publication Date

9-1-2024

Comments

Open Access; Hybrid Gold Open Access

Recommended Citation

Charan, Mrityunjoy and Vaishya, Lalit, "Construction of Jacobi forms using adjoint of the Jacobi–Serre derivative" (2024). Journal Articles. 4675.
https://digitalcommons.isical.ac.in/journal-articles/4675