摘要
Letλf(n)be the normalized n-th Fourier coefficient of holomorphic eigenform f for the full modular group and Pc(x):={p≤x|[pc]prime},c∈R+.In this paper,we show that for all 0<c<1 the mean value ofλf(n)in Pc(x)is x log-A x assuming the Riemann Hypothesis.Unconditionally,in the sense of Lebesgue measure,it holds for almost all c∈(ε,1-ε).
基金
Supported by National Natural Science Foundation of China(Grant Nos.11771256,11971476)。
