Generalized $L$-functions related to the Riemann zeta function

Kathrin Bringmann; Ben Kane; Srimathi Varadharajan

Generalized $L$-functions related to the Riemann zeta function

Number Theory 2023-05-23 v1

Authors: Kathrin Bringmann , Ben Kane , Srimathi Varadharajan

Abstract

In this paper, we construct generalized $L$ -functions associated to meromorphic modular forms of weight $\frac12$ for the theta group with a single simple pole in the fundamental domain. We then consider their behaviour towards $i\infty$ and relate this to the Riemann zeta function.

Keywords

zeta functions riemann zeta function theta correspondence

Cite

@article{arxiv.2305.13038,
  title  = {Generalized $L$-functions related to the Riemann zeta function},
  author = {Kathrin Bringmann and Ben Kane and Srimathi Varadharajan},
  journal= {arXiv preprint arXiv:2305.13038},
  year   = {2023}
}

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