论文标题
部分高斯总和和pólya-vinogradov的原始字符不等式
Partial Gaussian sums and the Pólya--Vinogradov inequality for primitive characters
论文作者
论文摘要
在本文中，我们为原始字符的Pólya-Vinogradov不等式获得了一个新的完全显式常数。给定一个原始字符$χ$ modulo $ q $，我们证明以下上限\ begin {align*} \ left | \sum_{1 \le n\le N} χ(n) \right|\le c \sqrt{q} \log q, \end{align*} where $c=3/(4π^2)+o_q(1)$ for even characters and $c=3/(8π)+o_q(1)$ for odd characters, with explicit $o_q(1)$ terms.这改善了Frolenkov和Soundararajan的结果，以$ Q $ $ Q $。在希尔德布兰德（Hildebrand）之后，我们继续获取蒙哥马利（Montgomery）的明确版本 - 沃恩（Vaughan）对部分高斯总和，并在复杂的dirichlet字符上获得了明显的汉堡般的结果。
In this paper we obtain a new fully explicit constant for the Pólya-Vinogradov inequality for primitive characters. Given a primitive character $χ$ modulo $q$, we prove the following upper bound \begin{align*} \left| \sum_{1 \le n\le N} χ(n) \right|\le c \sqrt{q} \log q, \end{align*} where $c=3/(4π^2)+o_q(1)$ for even characters and $c=3/(8π)+o_q(1)$ for odd characters, with explicit $o_q(1)$ terms. This improves a result of Frolenkov and Soundararajan for large $q$. We proceed, following Hildebrand, obtaining the explicit version of a result by Montgomery--Vaughan on partial Gaussian sums and an explicit Burgess-like result on convoluted Dirichlet characters.
