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

Kathrin Bringmann; Ben Kane

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arXiv · 2112.12943

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

Kathrin Bringmann·Ben Kane

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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.

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Kathrin Bringmann, Ben Kane. 2021-12-24. Generalized L-functions for meromorphic modular forms and their relation to the Riemann zeta function. https://arxiv.org/abs/2112.12943

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