The large sieve inequality with square moduli for quadratic extensions of function fields

TL;DR

This paper extends the large sieve inequality to square moduli within imaginary quadratic extensions of rational function fields, providing new bounds in the context of function fields over finite fields.

Contribution

It introduces a novel large sieve inequality for square moduli in quadratic extensions of function fields, expanding the scope of sieve methods in algebraic number theory.

Findings

Established a large sieve inequality for square moduli in quadratic extensions

Derived bounds applicable to function fields of odd characteristic

Extended classical sieve results to a new algebraic setting

Abstract

In this paper, we establish a version of the large sieve with square moduli for imaginary quadratic extensions of rational function fields of odd characteristics.