Large Sieve Inequalities with Quadratic Amplitudes

TL;DR

This paper introduces a new large sieve inequality involving quadratic amplitudes, utilizing the double large sieve technique to derive non-trivial bounds, advancing the understanding of sieve methods in number theory.

Contribution

It presents a novel large sieve inequality with quadratic amplitudes, applying the double large sieve to obtain new bounds in the field.

Findings

Established a large sieve inequality with quadratic amplitudes.

Derived non-trivial bounds using the double large sieve.

Enhanced techniques in sieve theory for quadratic cases.

Abstract

In this paper, we develop a large sieve type inequality with quadratic amplitude. We use the double large sieve to establish non-trivial bounds.