问题

Questions in category: 解析数论 (Analytic Number Theory).

证明 $\sum_{p}\{\ln(\frac{1}{1-\frac{1}{p}})-\frac{1}{p}\}$ 收敛

Posted by haifeng on 2017-09-11 21:19:38 last update 2018-09-30 20:55:22 | Answers (1) | 收藏

证明

\[
\sum_{p}\{\ln(\frac{1}{1-\frac{1}{p}})-\frac{1}{p}\}
\]

收敛.

References:

G. 特伦鲍姆 (Gérald Tenenbaum) 著《解析与概率数论导引》定理 1.9, P.17