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

Abstract

Let f be a normalized Hecke eigenform of weight k for the full modular group SL2(ℤ). In this paper, we obtain the asymptotic of higher moments of general divisor functions associated to the Fourier coefficients of Rankin-Selberg L-functions R(s,f × f), supported at the integers represented by primitive integral positive-definite binary quadratic forms (reduced forms) of a fixed discriminant D < 0. We improve previous results in the case when the reduced form is given by >(x1,x2) = x12 + x 22. © 2024 World Scientific Publishing Company.