The large sieve for self-dual Eisenstein series of varying levels

TL;DR

This paper establishes an essentially optimal large sieve inequality for self-dual Eisenstein series of varying levels, with implications for rationals ordered by height, using a recursive proof method.

Contribution

It introduces a new large sieve inequality for self-dual Eisenstein series that is nearly optimal and employs a recursive proof technique similar to existing quadratic and asymptotic sieves.

Findings

Proves an essentially optimal large sieve inequality for self-dual Eisenstein series.

Provides a new perspective on large sieve inequalities for rationals ordered by height.

Uses a recursive proof method with similarities to Heath-Brown and Conrey, Iwaniec, Soundararajan techniques.

Abstract

We prove an essentially optimal large sieve inequality for self-dual Eisenstein series of varying levels. This bound can alternatively be interpreted as a large sieve inequality for rationals ordered by height. The method of proof is recursive, and has some elements in common with Heath-Brown's quadratic large sieve, and the asymptotic large sieve of Conrey, Iwaniec, and Soundararajan.