GL(2)上自守L-函数的零点间隔北大核心CSCD

设f(z)是全模群SL_(2)(Z)上权为k的Hecke特征形式,L(s,f)为其对应的自守L-函数.利用此L-函数带有光滑化算子的二次积分均值,本文证明了L(s,f)在临界线上存在无穷多对零点,其间隔大于平均距离的1.88倍.     

Maass 尖形式对应的对称L- 函数的特殊值问题

Let {ø_j(z) : j ≥ 1} be an orthonormal basis of Hecke-Maass cusp forms with Laplace eigenvalue 1/4 + t_j². For each ø_j(z), we have the automorphic L-function L(s, sym²ø_j) which is called the symmetric square L-function associated to ø_j. In this paper, the average estimate of L(1/2, sym²ø_j) is considered, i.e., for sufficiently large T, the asymptotic formula
is established, where α_j is a certain fixed weight function and P(x) is a polynomial of degree 1.     

一类特殊Beatty序列中的素因子问题

研究了数论函数Ω和ω取值于一类特殊的非齐次Beatty序列[αn+β](n=1,2,…)的问题.特别地,证明了渐近公式∑ω([αn+β)=N log log N+O(N(log log N) )以及∑(一1)Ω(αn+β)=O( n/(log N 1/2)),其中α,β∈R,n∈Z+,α>0是型为1的无理数,Ω(k)和ω(k)表示整数k(≠0)的素因子个数(Ω记重数,ω不计重数).