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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Sums with convolutions of Dirichlet characters to cube-free modulus
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by Ahmet Muhtar Güloğlu PDF
Proc. Amer. Math. Soc. 139 (2011), 3195-3202 Request permission

Abstract:

We find estimates for short sums of the form $\sum _{nm \leqslant X} \chi _1 (n) \chi _2 (m)$, where $\chi _1$ and $\chi _2$ are non-principal Dirichlet characters to modulus $q$, a cube-free integer, and $X$ can be taken as small as $q^{\frac 12+\epsilon }$.
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Additional Information
  • Ahmet Muhtar Güloğlu
  • Affiliation: Department of Mathematics, Bilkent University, Bilkent, 06800 Ankara, Turkey
  • Email: guloglua@fen.bilkent.edu.tr
  • Received by editor(s): January 12, 2010
  • Received by editor(s) in revised form: August 21, 2010
  • Published electronically: February 3, 2011
  • Communicated by: Wen-Ching Winnie Li
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3195-3202
  • MSC (2010): Primary 11L40
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10753-6
  • MathSciNet review: 2811275