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

Diamantis, Nikolaos; Lee, Min; Raji, Wissam; Rolen, Larry

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.

Citation

Diamantis, N., Lee, M., Raji, W., & Rolen, L. (2022). L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts . International Mathematics Research Notices, Article rnac310. https://doi.org/10.1093/imrn/rnac310

• Journal Article Type: Article
• Acceptance Date: Oct 21, 2022
• Online Publication Date: Nov 14, 2022
• Publication Date: Nov 14, 2022
• Deposit Date: Nov 18, 2022
• Publicly Available Date: Nov 15, 2023
• Journal: International Mathematics Research Notices
• Print ISSN: 1073-7928
• Electronic ISSN: 1687-0247
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Article Number: rnac310
• DOI: https://doi.org/10.1093/imrn/rnac310
• Keywords: General Mathematics
• Public URL: https://nottingham-repository.worktribe.com/output/13751387
• Publisher URL: https://academic.oup.com/imrn/advance-article-abstract/doi/10.1093/imrn/rnac310/6827514?redirectedFrom=fulltext
• Additional Information: This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Nikolaos Diamantis, Min Lee, Wissam Raji, Larry Rolen, L-Series of Harmonic Maass Forms and a Summation Formula for Harmonic Lifts, International Mathematics Research Notices, 2022 is available online at: https://doi.org/10.1093/imrn/rnac310