Oscillations of Fourier coefficients of product of L-functions at integers in a sparse set

Abstract

Let [Formula: see text] be a normalized Hecke eigenform of weight [Formula: see text] for the full modular group [Formula: see text]. In this paper, we obtain the asymptotic of higher moments of general divisor functions associated to the Fourier coefficients of Rankin–Selberg [Formula: see text]-functions [Formula: see text], supported at the integers represented by primitive integral positive-definite binary quadratic forms (reduced forms) of a fixed discriminant [Formula: see text] We improve previous results in the case when the reduced form is given by [Formula: see text]