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On the higher mean over arithmetic progressions of Fourier coefficients of cusp forms
Let $\lambda_f(n)$ be the $n$th normalized Fourier coefficient of a holomorphic or Maass cusp form $f$ for $\mathrm{SL(2,\mathbb{Z})}$. We establish the asymptotic formula for the summatory function $$ \sum_{\substack{n\leq x \\ n\equiv l \,({\rm mod}\,