Generalized L-functions for meromorphic modular forms and their relation to the Riemann zeta function

2021/12/24 by Bringmann, Kathrin, Kane, Ben
#11F12 #11M06 #11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2112.12943

Abstract

In this paper, we construct a family of generalized L-functions, one for each point z in the upper half-plane. We prove that as z approaches i∞, these generalized L-functions converge to an L-function which can be written in terms of the Riemann zeta function.

Related

• Generalized L-functions related to the Riemann zeta function
• Meromorphic quasi-modular forms and their L-functions
• The standard L-function attached to a vector valued modular form
• The Fibonacci Zeta Function and Modular Forms
• Laurent series expansions of L-functions