Estimates of shifted convolution sums involving Fourier coefficients of Hecke–Maass eigenform

We obtain certain estimates for averages of shifted convolution sums involving the Fourier coefficients of a normalized Hecke–Maass eigenform and holomorphic cusp form.

Shifted convolution sums for higher rank groups

In this paper, we study some shifted convolution sums for higher rank groups. In particular, we establish an asymptotic formula for a {\mathrm{GL}(4)\times\mathrm{GL}(2)} shifted convolution sum\sum_{n\leq x}\lvert\lambda_{f}(n)\rvert^{2}r_{l}(n+b),where {\lambda_{f}(n)} are normalized Fourier coefficients of a Hecke holomorphic cusp form and {r_{l}(n)} denotes the number of representations of n by the quadratic form {x_{1}^{2}+\cdots+x_{l}^{2}}.