On shifted convolution sums of general divisor problem of Hecke eigenvalues

Let f be a normalized primitive holomorphic cusp form of even integral weight \(\kappa \) $\kappa$ for the full modular group \(\Gamma =SL(2,\mathbb {Z})\) $\mathrm{\Gamma }=SL(2,\mathbb{Z})$ . In this paper, we are interested in the averages of shifted convolution sums associated to general divisor sums involving the higher power moments of Hecke eigenvalues attached to f. We also obtain the analogous result for the coefficients of the Hecke–Maass cusp forms on \(\Gamma \) $\mathrm{\Gamma }$ under suitable assumptions.