论文标题
同时不散布与椭圆形形式相关的L功能的产物
Simultaneous nonvanishing of the Products of L-functions associated to elliptic cusp forms
论文作者
论文摘要
一个广义的Riemann假设指出，完整模块化组的正常hecke eigenform $ f $的完整hecke $ l $ l $ l $ -function $ l^*（f，s）$都应在垂直线上$ re re re（s）= \ frac {k} {k} {2} {k} {2}。对于足够大的$ k $而言，该$ l^*（f，s）\ neq 0 $以及行段$ im（s）= t_0，\ frac {k-1} {2} {2} <re（s）<\ frac {k} \ frac {k+1} {2}，对于任何给定的实际数字$ t_0 $和一个正实数$ε。
A generalized Riemann hypothesis states that all zeros of the completed Hecke $L$-function $L^*(f,s)$ of a normalized Hecke eigenform $f$ on the full modular group should lie on the vertical line $Re(s)=\frac{k}{2}.$ It was shown by Kohnen that there exists a Hecke eigenform $f$ of weight $k$ such that $L^*(f,s) \neq 0$ for sufficiently large $k$ and any point on the line segments $Im(s)=t_0, \frac{k-1}{2} < Re(s) < \frac{k}{2}-ε, \frac{k }{2}+ε< Re(s) < \frac{k+1}{2},$ for any given real number $t_0$ and a positive real number $ε.$ This paper concerns the non-vanishing of the product $L^*(f,s)L^*(f,w)$ $(s,w\in \mathbb{C})$ on average.
