Derivatives of L-series of weakly holomorphic cusp forms

2022/09/19 by Nikolaos Diamantis, Diamantis, Nikolaos, Fredrik Strömberg +1
Mathematics · #11F67 #11Y35 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2209.09229

openalex publication_date 2022/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on the theory of L-series associated with weakly holomorphic modular forms in \citeDLRR, 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.

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