On the sum of the twisted Fourier coefficients of Maass forms by Möbius function

In this paper, we study non-trivial upper bounds for the sum $\sum \limits_{n \in S} |λ_f(n)|$ where $f$ is a normalized Maass eigencusp form for the full modular group, $λ_f(n)$ is the $n$th normalized Fourier coefficient of $f$ and $S$ is a proper subset of positive integers in $[1,x]$ with certain properties.

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