Moments of derivatives of modular $L$-functions

Sumit Kumar; Kummari Mallesham; Prahlad Sharma; Saurabh Kumar Singh

Moments of derivatives of modular $L$-functions

Number Theory 2023-10-26 v2

Authors: Sumit Kumar , Kummari Mallesham , Prahlad Sharma , Saurabh Kumar Singh

Abstract

Let $f$ be an Hecke eigenform for the group $\Gamma_{0}(q)$ and $\chi_{d}$ be a primitive quadratic character of conductor $|d|$ . In this article, we prove an asymptotic for the second moment of the derivative of $L(s, f \otimes \chi_{8d})$ at the central point $1/2$ , which was previously known under GRH by Petrow \cite{petrow}.

Keywords

modular l-functions hecke eigenforms quadratic characters moments central point asymptotic

Cite

@article{arxiv.2303.16864,
  title  = {Moments of derivatives of modular $L$-functions},
  author = {Sumit Kumar and Kummari Mallesham and Prahlad Sharma and Saurabh Kumar Singh},
  journal= {arXiv preprint arXiv:2303.16864},
  year   = {2023}
}

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