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A generalization of the Pólya–Vinogradov inequality

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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.

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Acknowledgements

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.

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Authors and Affiliations

  1. Steklov Mathematical Institute, Gubkina str., 8, Moscow, 119991, Russia

    D. A. Frolenkov

  2. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    K. Soundararajan

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  1. D. A. Frolenkov
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  2. K. Soundararajan
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Correspondence to D. A. Frolenkov.

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Frolenkov, D.A., Soundararajan, K. A generalization of the Pólya–Vinogradov inequality. Ramanujan J 31, 271–279 (2013). https://doi.org/10.1007/s11139-012-9462-y

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

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