论文标题
pólya-短字符总和的Vinogradov不平等
A Pólya--Vinogradov inequality for short character sums
论文作者
论文摘要
在本文中，我们获得了pólya-vinogradov不平等的变化，总和仅限于一定高度。假设$χ$是原始角色模型$ q $，$ε> 0 $和$ n \ le q^{1-γ} $，带有$ 0 \leγ\ le 1/3 $。我们证明\ begin {equation*} \ left | \ sum_ {n = 1}^nχ（n）\ right | \ le c（\ frac {1} {1} {3} - γ+ε）\ sqrt {q} $ c = 1/π+o（1）$如果$χ$是奇数。
In this paper we obtain a variation of the Pólya--Vinogradov inequality with the sum restricted to a certain height. Assume $χ$ to be a primitive character modulo $q$, $ε> 0$ and $N\le q^{1-γ}$, with $0\le γ\le 1/3$. We prove that \begin{equation*} \left|\sum_{n=1}^N χ(n) \right|\le c(\frac{1}{3}-γ+ε)\sqrt{q}\log q \end{equation*} with $c=2/π^2+o(1)$ if $χ$ is even and $c=1/π+o(1)$ if $χ$ is odd.
