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Ramanujan J., 2013, Volume 31, Issue 3, Pages 271–279 (Mi ramaj1)  

A generalization of the Pólya–Vinogradov inequality

D. A. Frolenkova, K. Soundararajanb

a Steklov Mathematical Institute, Gubkina str., 8, Moscow 119991, Russia
b Department of Mathematics, Stanford University, Stanford CA 94305, USA

Abstract: In this paper we consider an approach of Dobrowolski and Williams which leads to a generalization of the Pólya–Vinogradov inequality. We show how the Dobrowolski–Williams approach is related to the classical proof of Pólya–Vinogradov using Fourier analysis. Our results improve upon the earlier work of Bachman and Rachakonda (Ramanujan J. 5:65–71, 2001). In passing, we also obtain sharper explicit versions of the Pólya–Vinogradov inequality.

Funding Agency Grant Number
Dynasty Foundation
Russian Foundation for Basic Research 11-01-00759-a
12-01-31165
National Science Foundation DMS-1001068
The First author is supported by the Dynasty Foundation, by the Russian Foundation for Basic Research (grants no. 11-01-00759-a and no. 12-01-31165). The second author is partially supported by NSF grant DMS-1001068.


DOI: https://doi.org/10.1007/s11139-012-9462-y


Bibliographic databases:

Document Type: Article
MSC: 11A25, 11L40
Received: 10.07.2011
Accepted:31.12.2012
Language: English

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