Large character sums: Pretentious characters and the Pólya-Vinogradov theorem
Large character sums: Pretentious characters and the Pólya-Vinogradov theorem
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DOI：
10.1090/s0894-0347-06-00536-4
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发表时间：
2005-03
影响因子：
3.9
通讯作者：
A. Granville;K. Soundararajan
中科院分区：
文献类型：
--
作者：
A. Granville;K. Soundararajan
1918年，Polya和Vinogradov给出了特征标和的最大值的一个上界，它仍然是最著名的一般估计。本文的主要结果之一是对奇数有界阶特征标的Polya-Vinogradov界作了实质性的改进。1977年，蒙哥马利和沃恩证明了在假设广义黎曼假设的情况下，波利亚-维诺格拉多夫不等式是如何被强化的。我们给出了它们估计的一个简单证明，并对奇数有界阶的特征标进行了改进。给出了特征和最大值较大的特征的刻画，发现了特征之间的隐含结构
In 1918 Polya and Vinogradov gave an upper bound for the maximal size of character sums, which still remains the best known general estimate. One of the main results of this paper provides a substantial improvement of the Polya-Vinogradov bound for characters of odd, bounded order. In 1977 Montgomery and Vaughan showed how the Polya-Vinogradov inequality may be sharpened assuming the Generalized Riemann Hypothesis. We give a simple proof of their estimate and provide an improvement for characters of odd, bounded order. The paper also gives characterizations of the characters for which the maximal character sum is large, and it finds a hidden structure among these characters