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

DOI10.1016/J.JMAA.2022.126623arXiv2112.12943MaRDI QIDQ6386617

Ben Kane, Kathrin Bringmann

Publication date: 23 December 2021

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

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Forms of half-integer weight; nonholomorphic modular forms (11F37) Langlands (L)-functions; one variable Dirichlet series and functional equations (11F66)

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