Uniform estimates for sums of coefficients of symmetric power L-functions.

Let f(z) be a holomorphic Hecke eigenform of even weight k for SL(2, ℤ), and denote by L(s, sym^mf) the corresponding symmetric power L-function associated with f. Denote by ⋋_sym^m_f (n) the nth normalized coefficient of L(s, sym^mf). In this paper, we investigate the sum Σ_n≤x⋋_sym^m_f (n) for m ≥ 2 and get the uniform upper bound extending the previous results. [ABSTRACT FROM AUTHOR]