On cycle integrals of weakly holomorphic modular forms

TL;DR

This paper explores cycle integrals of weakly holomorphic modular forms, demonstrating their equivalence to classical cusp form integrals and introducing a Shintani lift to connect different modular form spaces.

Contribution

It establishes the equality of cycle integrals between weakly holomorphic and cusp forms and defines a new Shintani lift for weakly holomorphic forms.

Findings

Cycle integrals of weakly holomorphic forms match those of cusp forms.

A new Shintani lift from integral to half-integral weight forms is introduced.

Results bridge weakly holomorphic and classical modular form theories.

Abstract

In this paper, we investigate cycle integrals of weakly holomorphic modular forms. We show that these integrals coincide with the cycle integrals of classical cusp forms. We use these results to define a Shintani lift from integral weight weakly holomorphic modular forms to half-integral weight holomorphic modular forms.