The large sieve for self-dual Eisenstein series of varying levels
Volume 214 / 2024
Acta Arithmetica 214 (2024), 39-88
MSC: Primary 11M06; Secondary 11N75
DOI: 10.4064/aa230213-1-1
Published online: 21 February 2024
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.
