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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sums with convolutions of Dirichlet characters to cube-free modulus


Author: Ahmet Muhtar Güloğlu
Journal: Proc. Amer. Math. Soc. 139 (2011), 3195-3202
MSC (2010): Primary 11L40
Published electronically: February 3, 2011
MathSciNet review: 2811275
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Abstract: We find estimates for short sums of the form $ \sum_{nm \le 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

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10753-6
PII: S 0002-9939(2011)10753-6
Keywords: Convolution of Dirichlet characters, Burgess bound
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.