Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficien...Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of Rankin-Selberg L-function L(f×f,s).This paper combines Kühleitner and Nowak′s Omega theorem and the analytic properties of Rankin-Selberg L-functions to study Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences,and establishes the asymptotic formula for Σ_(n≤x)λf×f(n^(m))(m=2,3).展开更多
Let λf(n) be the n-th normalized Fourier coefficient of a holomorphic Hecke eigenform f(z) ∈Sk(Γ).We establish that, for any ε > 0,1/Xintegral from n=1 to x|sum λ~2f^((n^2)) from n≤x to - c_2x|2dx ?ε X154/1...Let λf(n) be the n-th normalized Fourier coefficient of a holomorphic Hecke eigenform f(z) ∈Sk(Γ).We establish that, for any ε > 0,1/Xintegral from n=1 to x|sum λ~2f^((n^2)) from n≤x to - c_2x|2dx ?ε X154/101+ε,which improves previous results.展开更多
文摘Ω results involving the coefficients of automorphic L-functions are important research object in analytic number theory.Let f be a primitive holomorphic cusp form.Denote by λ_(f×f)(n) the nth Fourier coefficient of Rankin-Selberg L-function L(f×f,s).This paper combines Kühleitner and Nowak′s Omega theorem and the analytic properties of Rankin-Selberg L-functions to study Omega results for coefficients of Rankin-Selberg L-functions over sparse sequences,and establishes the asymptotic formula for Σ_(n≤x)λf×f(n^(m))(m=2,3).
基金supported by National Natural Science Foundation of China (Grant Nos.11026075, 10971119)the Natural Science Foundation of Shandong Province (Grant No. ZR2009AQ007)
文摘We prove a non-trivial upper bound for the quantity ∫X2|X ∑_(n≤x)λ~2(nj)-c(j-1)x| 2dx for j=2, 3, 4.
基金supported by National Natural Science Foundation of China(Grant No.11101249)
文摘Let λf(n) be the n-th normalized Fourier coefficient of a holomorphic Hecke eigenform f(z) ∈Sk(Γ).We establish that, for any ε > 0,1/Xintegral from n=1 to x|sum λ~2f^((n^2)) from n≤x to - c_2x|2dx ?ε X154/101+ε,which improves previous results.
