Estimates for the Fourier coefficients of symmetric square L-functions

摘要

Let f(z) be a holomorphic Hecke eigenform of even weight k for the full modular group SL_2(?), and denote by L(s, sym~2f) the corresponding symmetric square L-function associated to f. Suppose that λ_(sym~2f)(n) is the nth normalized Fourier coefficient of L(s, sym~2~f). In this paper, the asymptotic formula is established.