On the Distribution of Hecke Eigenvalues over Piatetski-Shapiro Prime Twins

• 作者: De Yu ZHANG Wen Guang ZHAI
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2021,（9）
• 页码范围: 1453-1464
• 页数: 12页
• 语种: 英文

摘要

Let λf (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 of λf (n) in Pc (x) is ＜＜ x 1og-A x assuming the Riemann Hypothesis.Unconditionally,in the sense of Lebesgue measure,it holds for almost all c ∈ (ε,1-ε).