Algebraic Number Theory
《Algebraic Number Theory》 · 第 307 页 · Section 9.4，Theorem 9.18
The Pólya–Vinogradov inequality. Let $\chi$ be a non-principal character modulo $q$. Then for any integers $M$ and $N$ with $N>0$, $\sum_{n=M+1}^{M+N}\chi(n)\ll\sqrt q\log q$.