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Register a new userNon-linear additive twist of Fourier coefficients of $GL(3)$ Maass forms
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Let $lambda_{pi}(1,n)$ be the Fourier coefficients of the Hecke-Maass cusp form $pi$ for $SL(3,mathbb{Z})$. The aim of this article is to get a non trivial bound on the sum which is non-linear additive twist of the coefficients $lambda_{pi}(1,n)$. More precisely, for any $0 < beta < 1$ we have $$sum_{n=1}^{infty} lambda_{pi}(1,n) , eleft(alpha n^{beta}right) Vleft(frac{n}{X}right) ll_{pi, alpha,epsilon} X^{frac{3 }{4}+frac{3 beta}{10} + epsilon}$$ for any $epsilon>0$. Here $V(x)$ is a smooth function supported in $[1,2]$ and satisfies $V^{(j)}(x) ll_{j} 1$.
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