The large sieve for square moduli in function fields

TL;DR

This paper establishes bounds for the large sieve with square moduli in function fields, comparing them to classical results and identifying an error in previous work.

Contribution

It provides new bounds for the large sieve in the function field setting and corrects a mistake in earlier research.

Findings

Bounds for the large sieve with square moduli in function fields are established.

The lower bound contradicts a previously claimed upper bound, revealing an error in earlier work.

The results align with classical large sieve bounds, extending them to function fields.

Abstract

We prove a lower and an upper bound for the large sieve with square moduli for function fields. These bounds correspond to bounds for the classical large sieve with square moduli established in arXiv:1812.05844 by Baier, Lynch and Zhao and arXiv:math/0512271 by Baier and Zhao. Our lower bound in the function field setting contradicts an upper bound obtained in arXiv:1802.03131 by Baier and Singh. Indeed, we point out an error in arXiv:1802.03131.