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

Kathrin Bringmann; Ben Kane

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

Number Theory 2021-12-28 v1

Authors: Kathrin Bringmann , Ben Kane

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 $i\infty$ , these generalized $L$ -functions converge to an $L$ -function which can be written in terms of the Riemann zeta function.

Keywords

zeta functions riemann zeta function l-functions

Cite

@article{arxiv.2112.12943,
  title  = {Generalized L-functions for meromorphic modular forms and their relation to the Riemann zeta function},
  author = {Kathrin Bringmann and Ben Kane},
  journal= {arXiv preprint arXiv:2112.12943},
  year   = {2021}
}

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