A note on the Fourier coefficients of Hecke-Maass forms

作者：Tang Hengcai^*

来源：Journal of Number Theory, 2013, 133(4): 1156-1167.

DOI：10.1016/j.jnt.2012.09.009

• Fourier coefficients of cusp forms
• Symmetric square L-function
• Rankin-Selberg L-function

To a Hecke-Maass form f(z) with Laplace eigenvalue 1/4 + nu(2), we have an automorphic L-function L(s, sym(2) f) which is called the symmetric square L-function associated to f. Suppose that lambda(sym2) (f)(n) is the nth Fourier coefficient of L(s, sym(2) f). In this paper, the estimate
Sigma(n <= x)lambda(sym2) f(n) << nu(3/4+epsilon)x(1/2+epsilon) + x(39/64+epsilon)
is established.

• 出版日期2013-4
• 单位河南大学