Modular Forms on the Double Half-Plane

TL;DR

This paper introduces a new concept of modular forms on the double half-plane for half-integral weights, linking it to classical modular forms and considering physical motivations.

Contribution

It defines modular forms on the double half-plane for half-integral weights and explores their relation to traditional modular forms, incorporating physical considerations.

Findings

Established a formal definition of modular forms on the double half-plane.

Connected the new notion to classical modular forms.

Addressed physical motivations in the construction.

Abstract

We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to the second author.