Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,an...Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).展开更多
In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. ...In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.展开更多
基金Supported by Natural Science Foundation of Shandong Province(No.ZR2024MA053)。
文摘Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).
基金Supported by the National Key R&D Program of China(Grant No.2021YFA1000700)National Natural Science Foundation of China(Grant No.12031008)。
文摘In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.
基金Supported by the National Naural Science Foundation of China (1 0 3 71 0 65 ) InitiationFoundation for Ph.D of Univ.ersity.of Shanghai for Science and Technology(X45 1 )
