Rankin-Selberg coefficients in large arithmetic progressions

Abstract

Let (λf (n))n⩾1 be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f. We prove that, for any fixed η > 0, under the Ramanujan-Petersson conjecture for GL2 Maass forms, the Rankin-Selberg coefficients (λf (n)2)n⩾1 admit a level of distribution θ = 2/5 + 1/260 − η in arithmetic progressions.