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Let $\Lambda(1,n)$ be the $(1,n)$-th Fourier coefficients of$SL(3,\mathbb{Z})$ Hecke-Maass cusp form and $d_3(n)$ denotes the tripledivisor function. This paper establishes non-trivial bounds for the averages ofthese arithmetic functions over polynomials in three variables having mixedpowers and over quadratic forms.

Sum of the $GL(3)$ Fourier coefficients over quadratics and mixed powers