An improved spectral large sieve inequality for ${\rm SL}_3(\mathbb {Z})$
Volume 204 / 2022
Acta Arithmetica 204 (2022), 151-164
MSC: Primary 11F03; Secondary 11F55, 11F72, 11M41.
DOI: 10.4064/aa211008-29-4
Published online: 20 June 2022
Abstract
We prove an improved spectral large sieve inequality for the family of ${\rm SL }_3(\mathbb {Z})$ Hecke–Maass cusp forms. The method of proof uses duality, and its structure reveals unexpected connections to Heath-Brown’s large sieve for cubic characters.
