<i>L</i>-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts-Reference-Cited by-同舟云学术

L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts

Published:2022-11-14 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Diamantis Nikolaos¹,Lee Min²,Raji Wissam³,Rolen Larry⁴

Affiliation:

1. School of Mathematical Sciences, University of Nottingham , University Park, Nottingham. NG7 2RD, United Kingdom

2. School of Mathematics, University of Bristol , Fry Building, Woodland Road, BS8 1UG, United Kingdom

3. Department of Mathematics, American University of Beirut , Riad El Solh, Beirut 1107 2020, Lebanon

4. Department of Mathematics, 1420 Stevenson Center, Vanderbilt University , Nashville, TN 37240, USA

Abstract

Abstract We introduce an $L$-series associated with harmonic Maass forms and prove their functional equations. We establish converse theorems for these $L$-series and, as an application, we formulate and prove a summation formula for the holomorphic part of a harmonic lift of a given cusp form.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnac310/49545536/rnac310.pdf

Reference20 articles.

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3. American Mathematical Society Colloquium Publications;Bringmann,2017

4. Special $L$-values and periods of weakly holomorphic modular forms;Bringmann;Proc. Amer. Math. Soc.,2014

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1. L-series of weakly holomorphic quasimodular forms and a converse theorem;Forum Mathematicum;2024-01-03

2. Analogues of the Bol operator for half-integral weight weakly holomorphic modular forms;Proceedings of the American Mathematical Society;2023-10-24

3. -values of harmonic Maass forms;T AM MATH SOC;2023-09-02