Derivatives of L-series of weakly holomorphic cusp forms

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.