An improved large sieve for quadratic characters via Hooley neutralisers and its applications

TL;DR

This paper introduces an enhanced large sieve technique for quadratic characters by integrating Hooley neutralisers, leading to new applications in character sums constrained by hyperbolic height conditions.

Contribution

It presents a novel combination of Hooley neutralisers with the large sieve for quadratic characters, advancing the analytical tools available for character sum estimates.

Findings

Improved bounds for quadratic character sums under hyperbolic height conditions

New applications of the combined sieve method in number theory

Enhanced understanding of quadratic character distributions

Abstract

We combine Hooley neutralisers and the large sieve for quadratic characters. We give applications to character sums with a hyperbolic height condition.