Derivatives of L-series of weakly holomorphic cusp forms

Diamantis, Nikolaos; Stromberg, Fredrik

Abstract

Based on the theory of L-series associated with weakly holomorphic modular forms in Diamantis et al. (L-series of harmonic Maass forms and a summation formula for harmonic lifts. arXiv:2107.12366), we derive explicit formulas for central values of derivatives of L-series as integrals with limits inside the upper half-plane. This has computational advantages, already in the case of classical holomorphic cusp forms and, in the last section, we discuss computational aspects and explicit examples.

Citation

Diamantis, N., & Stromberg, F. (2022). Derivatives of L-series of weakly holomorphic cusp forms. Research in the Mathematical Sciences, 9(4), Article 64. https://doi.org/10.1007/s40687-022-00363-x

• Journal Article Type: Article
• Acceptance Date: Oct 10, 2022
• Online Publication Date: Oct 26, 2022
• Publication Date: Oct 26, 2022
• Deposit Date: Oct 10, 2022
• Publicly Available Date: Oct 27, 2023
• Journal: Research in the Mathematical Sciences
• Electronic ISSN: 2197-9847
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Issue: 4
• Article Number: 64
• DOI: https://doi.org/10.1007/s40687-022-00363-x
• Keywords: Applied Mathematics; Computational Mathematics; Mathematics (miscellaneous); Theoretical Computer Science
• Public URL: https://nottingham-repository.worktribe.com/output/12320087
• Publisher URL: https://link.springer.com/article/10.1007/s40687-022-00363-x