论文标题
请注意$ζ^{（k）}（s）$的零数
Note on the number of zeros of $ζ^{(k)}(s)$
论文作者
论文摘要
假设假设假设，我们证明$$ n_k（t）= \ frac {t} {2π} \ log \ frac {t} {4πe} + o_k \ left（\ frac {\ frac {\ log log {t}}} $ζ^{（k）}（s）$的零$ 0 <\ im s \ le t $。我们进一步应用我们的方法，并为Selberg Zeta函数的导数获得零计数公式，从而改善了LUO的早期工作。
Assuming the Riemann hypothesis, we prove that $$ N_k(T) = \frac{T}{2π}\log \frac{T}{4πe} + O_k\left(\frac{\log{T}}{\log\log{T}}\right), $$ where $N_k(T)$ is the number of zeros of $ζ^{(k)}(s)$ in the region $0<\Im s\le T$. We further apply our method and obtain a zero counting formula for the derivative of Selberg zeta functions, improving earlier work of Luo.
