Moment of derivatives of L-functions for two distinct newforms

TL;DR

This paper proves an unconditional asymptotic formula for the moments of derivatives of products of L-functions associated with two distinct newforms over quadratic twists.

Contribution

It provides the first unconditional asymptotic formula for these moments, advancing understanding of L-functions and their derivatives in the context of quadratic twists.

Findings

Established an unconditional asymptotic formula for the moments of derivatives of L-functions.

Extended the analysis to products of L-functions associated with two distinct newforms.

Contributed to the theoretical understanding of L-functions in number theory.

Abstract

We establish an unconditional result concerning the asymptotic formula for the moment of derivatives of $L$-functions $L(s, f \otimes \chi_{8d})L(s, g \otimes \chi_{8d})$ over quadratic twists, where $f$ and $g$ are distinct cuspidal newforms.