Shifted convolution sums of fourier coefficients with <i>k</i>-full kernel functions

We study the behavior of the shifted convolution sum involving fourth power of the Fourier coefficients of holomorphic cusp forms with a weight function to be the k-full kernel function for any fixed integer [Formula: see text]. In this paper, we will generalize the problem of Lü and Wang [Shifted convolution sums of Fourier coefficients with square-full kernel functions, Lithuanian Math. J. 60 (2020) 51–63], and improve the results of Venkatasubbareddy and Sankaranarayanan [On certain kernel functions and shifted convolution sums of Fourier coefficients, J. Number Theory 258 (2024) 414–450], the error term from [Formula: see text] to [Formula: see text].