Bilinear forms with Kloosterman and Gauss sums in function fields

2023/04/11 by Bagshaw, Christian
#11T06 #11T23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2304.05014

Abstract

In recent years, there has been a lot of progress in obtaining non-trivial bounds for bilinear forms of Kloosterman sums in ℤ/mℤ 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 \mathbbF_q[T] .

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