Large sieve inequality with power moduli for function fields

TL;DR

This paper develops a generalized large sieve inequality with additive characters for function fields, extending it to high dimensions and power moduli, providing a versatile tool for analytic number theory in function fields.

Contribution

It introduces a broad large sieve inequality applicable to restricted moduli sets in arbitrary dimensions for function fields, including power moduli cases.

Findings

Established a general large sieve inequality for function fields

Extended the inequality to high-dimensional settings

Derived specific results for power moduli

Abstract

In this paper, we establish a general version of the large sieve with additive characters for restricted sets of moduli in arbitrary dimension for function fields. From this, we derive function field versions for the large sieve in high dimensions and for power moduli.