On the Constant in the Pólya-Vinogradov Inequality

Author:

Hildebrand Adolf

Abstract

AbstractThe Pólya-Vinogradov inequality states that for any non-principal character x modulo q and any N ≧ 1,where c is an absolute constant. We show that (*) holds with c = 2/(3π2) + o(1) in the case x is primitive and x (— 1) =1 with c = 1/(3π) + o(l) in the case x is primitive and x(— 1) = — 1- This improves by a factor 2/3 the previously best-known values for these constants.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 15 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Partial Gaussian sums and the Pólya–Vinogradov inequality for primitive characters;Revista Matemática Iberoamericana;2021-12-13

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3. A Pólya–Vinogradov inequality for short character sums;Canadian Mathematical Bulletin;2020-12-02

4. An explicit Pólya-Vinogradov inequality via Partial Gaussian sums;Transactions of the American Mathematical Society;2020-07-08

5. On the constant in the Pólya-Vinogradov inequality;Journal of Number Theory;2020-07

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