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arXiv · 2608.11611

Upper bound for the moment of shifted values of cubic $L$-functions over function fields

Pranendu Darbar·Sampa Dey·Gopal Maiti
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Abstract

In this paper, we study correlations of shifted values of cubic $L$-functions over function fields and derive an upper bound for moments of these shifted values in the limit where the genus of the corresponding cubic characters tends to infinity over a fixed finite field $\mathbb{F}_q$. Our results apply to the non-Kummer case when $q \equiv 2 \pmod{3}$. The Kummer case, when $q \equiv 1 \pmod{3}$, can be treated similarly.

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Pranendu Darbar, Sampa Dey, Gopal Maiti. 2026-08-12. Upper bound for the moment of shifted values of cubic $L$-functions over function fields. https://arxiv.org/abs/2608.11611

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