
doi: 10.1007/bf02395024
Für eine monotone Folge reeller Zahlen \(1 0\), derart daß für jedes \(n >0\) gilt: \[ N(x) = ax + O\left\{\frac{x}{(\log x)^n}\right\},\quad\text{falls}\quad x\to\infty. \] B. Zu jedem \(\varepsilon >0\) und jedem ganzen \(n\ge 0\) gibt es eine Konstante \(A\) derart, daß \[ \left\vert \zeta^{(n)}(s)\right\vert 1\), \(\vert t\vert\ge \varepsilon\). C. Für jedes positive \(n\) ist \[ \pi(x) = \operatorname{Li}(x) + O\left\{\frac{x}{(\log x)^n}\right\},\quad\text{falls}\quad x\to\infty. \]
Multiplicative number theory, general prime number theorem
Multiplicative number theory, general prime number theorem
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