Explicit quadratic large sieve inequality

TL;DR

This paper presents an explicit form of Heath-Brown's large sieve inequality tailored for quadratic characters, enhancing tools for analyzing $L$-functions and quadratic fields with potential applications in number theory.

Contribution

It provides the first explicit version of the quadratic large sieve inequality, improving upon previous implicit bounds and enabling more precise applications.

Findings

Derived an explicit inequality for quadratic characters

Applied the inequality to $L$-functions and quadratic fields

Improved bounds in related number theory problems

Abstract

In this article, we obtain an explicit version of Heath-Brown's large sieve inequality for quadratic characters and discuss its applications to $L$-functions and quadratic fields.