Moments of quadratic Dirichlet character sums

Yuichiro Toma

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arXiv · 2502.19905

Moments of quadratic Dirichlet character sums

Yuichiro Toma

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Abstract

We consider moments of higher powers of quadratic Dirichlet character sums. In a restricted region, we give their asymptotic behavior by using de la Bret\`{e}che's multivariable Tauberian theorem. We also give the lower bound of the exponent of $\log$ factor in the conjecture of Jutila. As an application, we give a lower bound of a weighted average of shifted moments of quadratic Dirichlet $L$-functions.

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Yuichiro Toma. 2025-02-27. Moments of quadratic Dirichlet character sums. https://arxiv.org/abs/2502.19905

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