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arXiv · 2304.05014

Bilinear forms with Kloosterman and Gauss sums in function fields

Christian Bagshaw
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Abstract

In recent years, there has been a lot of progress in obtaining non-trivial bounds for bilinear forms of Kloosterman sums in $\mathbb{Z}/m\mathbb{Z}$ for arbitrary integers $m$. These results have been motivated by a wide variety of applications, such as improved asymptotic formulas for moments of $L$-functions. However, there has been very little work done in this area in the setting of rational function fields over finite fields. We remedy this and provide a number of new non-trivial bounds for bilinear forms of Kloosterman and Gauss sums in this setting, based on new bounds on the number of solutions to certain modular congruences in $\mathbb{F}_q[T]$ .

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Christian Bagshaw. 2023-04-11. Bilinear forms with Kloosterman and Gauss sums in function fields. https://arxiv.org/abs/2304.05014

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