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arXiv · 2303.16864

Moments of derivatives of modular $L$-functions

Sumit Kumar·Kummari Mallesham·Prahlad Sharma·Saurabh Kumar Singh
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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}.

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Sumit Kumar, Kummari Mallesham, Prahlad Sharma, Saurabh Kumar Singh. 2023-03-29. Moments of derivatives of modular $L$-functions. https://arxiv.org/abs/2303.16864

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