论文标题
Riemann Zeta功能的非平凡零的谐波总和
A harmonic sum over nontrivial zeros of the Riemann zeta-function
论文作者
论文摘要
我们考虑总和1/γ$，其中$γ$在riemann zeta-function的非平凡零的尺寸上以$（0，t] $为准），并考虑总和作为$ t \ to \ infty $的行为。 \ log^2（t/2π），$总和可以使用具有错误$ O（（\ log log t）/t^2）的方法来表达的$ h \约-0.0171594 $。
We consider the sum $\sum 1/γ$, where $γ$ ranges over the ordinates of nontrivial zeros of the Riemann zeta-function in an interval $(0,T]$, and consider the behaviour of the sum as $T \to\infty$. We show that, after subtracting a smooth approximation $\frac{1}{4π} \log^2(T/2π),$ the sum tends to a limit $H \approx -0.0171594$ which can be expressed as an integral. We calculate $H$ to high accuracy, using a method which has error $O((\log T)/T^2)$. Our results improve on earlier results by Hassani and other authors.
