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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 | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)

  • 1. W. D. Banks, I. Shparlinski, Sums with convolutions of Dirichlet characters, preprint, 2009.
  • 2. D. A. Burgess, On character sums and 𝐿-series. II, Proc. London Math. Soc. (3) 13 (1963), 524–536. MR 0148626
  • 3. John B. Friedlander and Henryk Iwaniec, Summation formulae for coefficients of 𝐿-functions, Canad. J. Math. 57 (2005), no. 3, 494–505. MR 2134400, 10.4153/CJM-2005-021-5
  • 4. Henryk Iwaniec and Emmanuel Kowalski, Analytic number theory, American Mathematical Society Colloquium Publications, vol. 53, American Mathematical Society, Providence, RI, 2004. MR 2061214
  • 5. N. G. Moshchevitin, Sets of the form 𝒜+ℬ and finite continued fractions, Mat. Sb. 198 (2007), no. 4, 95–116 (Russian, with Russian summary); English transl., Sb. Math. 198 (2007), no. 3-4, 537–557. MR 2352362, 10.1070/SM2007v198n04ABEH003848
  • 6. N. G. Moshchevitin and D. M. Ushanov, On Larcher's theorem concerning good lattice points and multiplicative subgroups modulo $ p$, Unif. Distrib. Theory 5 (1) (2010), 45-52.

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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
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.