Affiliation:
1. School of Mathematics and Statistics, Weinan Normal University, Shaanxi, Weinan, China + School of Mathematics, Shandong University, Shandong, Jinan, China
Abstract
Let f be a normalized primitive holomorphic cusp form of even integral weight
for the full modular group ? = SL(2,Z), and let ?f (n), ?(n) and ?(n) be the
nth normalized Fourier coefficient of the cusp form f , the sum-of-divisors
function and the Euler totient function, respectively. In this paper, we
investigate the asymptotic behaviour of the following summatory function
Sj,b,c(x) := X n=a21 +a22 +a23 +a24 ?x (a1,a2,a3,a4)?Z4 ?j f (n)?b(n)?c(n),
where j ? 2 is any given integer. In a similar manner, we also establish
other similar results related to normalized coefficients of the symmetric
power L-functions associated to holomorphic cusp form f.
Publisher
National Library of Serbia
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