A decomposition of the Fourier-Jacobi coefficients of Klingen Eisenstein series

TL;DR

This paper explores the relationship between two decompositions of modular form spaces, linking Klingen's and Dulinski's approaches for Siegel and Jacobi forms, respectively.

Contribution

It establishes a connection between Klingen's and Dulinski's decompositions, enhancing understanding of the structure of modular form spaces.

Findings

Identifies the correspondence between Klingen and Dulinski decompositions.

Provides a new perspective on the structure of Siegel and Jacobi modular forms.

Clarifies the relationship between different modular form decompositions.

Abstract

We investigate the relation between Klingen's decomposition of the space of Siegel modular forms and Dulinski's analogous decomposition of the space of Jacobi forms.