Meromorphic quasi-modular forms and their $L$-functions

TL;DR

This paper explores the properties of meromorphic quasi-modular forms and their associated $L$-functions, providing explicit formulas and vanishing results for special values, advancing understanding in modular forms and number theory.

Contribution

It introduces a new approach to defining $L$-functions for meromorphic quasi-modular forms using regularized integrals and derives explicit formulas and vanishing results.

Findings

Explicit formulas for $L$-functions of meromorphic quasi-modular forms

Vanishing results for certain special $L$-values

Development of a regularized integral technique for these forms

Abstract

We investigate the meromorphic quasi-modular forms and their $L$-functions. We study the space of meromorphic quasi-modular forms. Then we define their $L$-functions by using the technique of regularized integral. Moreover, we give an explicit formula for the $L$-functions. As an application, we obtain some vanishing results of special $L$-values of meromorphic quasi-modular forms.