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L-series for Vector-Valued Weakly Holomorphic Modular Forms and Converse Theorems

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  21 January 2025

Subong Lim  and
Wissam Raji
Subong Lim
Affiliation:
Department of Mathematics Education, Sungkyunkwan University, Jongno-gu, Seoul 110-745, Republic of Korea subong@skku.edu
Wissam Raji*
Affiliation:
Department of Mathematics, American University of Beirut (AUB) and the Number Theory Research Unit at the Center for Advanced Mathematical Sciences (CAMS) at AUB, Beirut, Lebanon
*
e-mail: wr07@aub.edu.lb
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Abstract

We introduce the L-series of weakly holomorphic modular forms using Laplace transforms and give their functional equations. We then determine converse theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and elliptic modular forms of half-integral weight in Kohnen plus space.

Keywords

L-seriesweakly holomorphic modular formsLaplace transofrms

MSC classification

Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 11F50: Jacobi forms 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 26
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The first-named author was supported by the National Research Foundation of Korea (NRF) grant, which was funded by the Korea government(MSIT) (Grant No. RS-2024-00346031).

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