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arXiv · 2410.20144

On the Second Moment of Twisted Higher Degree $L$-functions

Haozhe Gou·Liangxun Li
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Abstract

Assuming the Ramanujan conjecture, the zero density estimate and some subconvexity type bound, we describe a general method to obtain the log-saving upper bound for the second moment of standard twisted higher degree $L$-function in the $q$-aspect. Specifically, let $L(s, F)$ be a standard $L$-function of degree $d\geq3$. Under these foundational hypotheses. the bound \[ \sideset{}{^*}{\sum}_{\chi \pmod q}\Big|L\big(\frac{1}{2}, F\times \chi \big)\Big |^2\ll_{F,\eta} \frac{q^{\frac{d}{2}}}{\log^{\eta}q} \] holds for some small $\eta>0$

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Haozhe Gou, Liangxun Li. 2024-10-26. On the Second Moment of Twisted Higher Degree $L$-functions. https://arxiv.org/abs/2410.20144

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