Shifted convolution sums of divisor functions with Fourier coefficients

Abstract

Let f(z) be a holomorphic cusp form of weight κ for the full modular group SL2(Z). Denote its n-th normalized Fourier coefficient by λf(n). Let τk(n) denote that k-th divisor function with k≥4. In this paper, we consider the shifted convolution sum∑n≤Xτk(n)λf(n+h). We succeed in obtaining a non-trivial upper bound, which is uniform in the shift parameter h.