论文标题
Riemann Zeta功能的非平凡零的加权一级密度
A weighted one-level density of the non-trivial zeros of the Riemann zeta-function
论文作者
论文摘要
我们计算由$ |ζ（\ frac12+it）加权的Riemann Zeta功能的非平凡零的一级密度（$ k = 1 $）|^{2k} $，对于$ k = 1 $，对于$ k = 1 $的测试函数，$ k = 1 $（$ \ frac12，\ frac12），\ frac12 $，for $ k = 2 $ k = 2 $ k = 2 $ k = 2 $ k = 2 $。结果，对于$ k = 1,2 $，我们根据Riemann假设推断出$ t（\ log t）^{1-k^2+o（1）} $ $ζ$的非客气零，假想零件的$ t $最高为$ t $，是$ζ$在$ qual中的价值，是$（\ log t）的价值（\ log log t t） $ O（1/\ log t）$来自零。
We compute the one-level density of the non-trivial zeros of the Riemann zeta-function weighted by $|ζ(\frac12+it)|^{2k}$ for $k=1$ and, for test functions with Fourier support in $(-\frac12,\frac12)$, for $k=2$. As a consequence, for $k=1,2$, we deduce under the Riemann hypothesis that $T(\log T)^{1-k^2+o(1)}$ non-trivial zeros of $ζ$, of imaginary parts up to $T$, are such that $ζ$ attains a value of size $(\log T)^{k+o(1)}$ at a point which is within $O(1/\log T)$ from the zero.
