Modified Jacobi forms of index zero

TL;DR

This paper introduces modified Jacobi forms of index zero, which generate nearly holomorphic modular forms and lead to the construction of finite-dimensional subspace families through Fourier coefficient analysis.

Contribution

It defines a new class of modified Jacobi forms of index zero and explores their role in generating nearly holomorphic modular forms and constructing finite-dimensional subspaces.

Findings

Modified Jacobi forms of index zero are introduced.

These forms generate nearly holomorphic modular forms.

A family of finite-dimensional subspaces is constructed.

Abstract

By modifying a slash operator of index zero we define \textit{modified Jacobi forms} of \textit{index zero}. Such forms play a role of generating nearly holomorphic modular forms of integral weight. Furthermore, by observing a relation between the coefficients of Fourier development of a modified Jacobi form we construct a family of finite-dimensional subspaces.