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arXiv · 2109.05708

Correlation of shifted values of $L$-functions in the hyperelliptic ensemble

Pranendu Darbar·Gopal Maiti
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Abstract

The moments of quadratic Dirichlet $L$-functions over function fields have recently attracted much attention with the work of Andrade and Keating. In this article, we establish lower bounds for the mean values of the product of quadratic Dirichlet $L$-functions associated with hyperelliptic curves of genus $g$ over a fixed finite field $\mathbb{F}_q$ in the large genus limit. By using the idea of A. Florea \cite{FL3}, we also obtain their upper bounds. As a consequence, we find upper bounds of its derivatives. These lower and upper bounds give the correlation of quadratic Dirichlet $L$-functions associated with hyperelliptic curves with different transitions.

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Pranendu Darbar, Gopal Maiti. 2021-09-13. Correlation of shifted values of $L$-functions in the hyperelliptic ensemble. https://arxiv.org/abs/2109.05708

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