Jacobi forms of degree one

TL;DR

This paper establishes an explicit isomorphism between subspaces of elliptic cusp forms and Jacobi cusp forms of degree one, extending previous work and connecting with Ikeda lifting.

Contribution

It constructs a new explicit lifting that generalizes Skoruppa and Zagier's work and relates to Ikeda lifting.

Findings

Identifies an isomorphism as Hecke modules between elliptic and Jacobi cusp forms.

Provides an explicit construction of the lifting.

Extends the understanding of the relationship between different types of modular forms.

Abstract

We show that a certain subspace of space of elliptic cusp forms is isomorphic as a Hecke module to a certain subspace of space of Jacobi cusp forms of degree one with matrix index by constructing an explicit lifting. This is a partial generalization of the work of Skoruppa and Zagier. This lifting is also related with the Ikeda lifting.