Let f be a Hecke eigencusp form of even integral weight k or Maass cusp form for the full modular group SL 2 (Z). Denote by λ sym m f (n) the nth normalized coefficient of the Dirichlet expansion of the mth symmetric power Lfunction associated to f . In this paper, we establish some bounds for n x λ sym m f (n), n x λ f (n m ), which improve the corresponding results of Lau & Lü [9].
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