Algebraic Number Theory
《Algebraic Number Theory》 · 第 138 页 · Section 5.1「The inverse Mellin transform」, Theorem 5.1
Theorem 5.1 (Perron's formula) If $\sigma_0>\max(0,\sigma_c)$ and $x>0$, then $\sum_{n\le x}'a_n=\lim_{T\to\infty}\frac1{2\pi i}\int_{\sigma_0-iT}^{\sigma_0+iT}\alpha(s)\frac{x^s}{s}\,ds$.