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A slight improvement to Garaev's sum product estimate


Authors: Nets Hawk Katz and Chun-Yen Shen
Journal: Proc. Amer. Math. Soc. 136 (2008), 2499-2504
MSC (2000): Primary 42B25; Secondary 60K35
DOI: https://doi.org/10.1090/S0002-9939-08-09385-4
Published electronically: March 10, 2008
MathSciNet review: 2390519
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References [Enhancements On Off] (What's this?)

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  • [BKT] Bourgain, J., Katz, N., and Tao, T., A sum-product estimate in finite fields and applications, Geom. Funct. Anal. 14 (2004), 27-57. MR 2053599 (2005d:11028)
  • [G1] Garaev, M.Z., An explicit sum-product estimate in $ \mathbb{F}_{p}$, preprint, http://arxiv.org/ abs/math/0702780.
  • [G2] Garaev, M.Z., The sum product estimate for large subsets of prime orders, preprint, http://arxiv.org/abs/0706.0702.
  • [GK] Glibichuk, A.A., and Konyagin, S.V., Additive properties of product sets in fields of prime order, preprint.
  • [S] Solymosi, J., On the number of sums and products, Bull. London Math. Soc. 37 (2005), 491-494. MR 2143727 (2006c:11021)
  • [TV] Tao, T. and Vu, V., Additive Combinatorics, Cambridge Univ. Press, 2006. MR 2289012

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Additional Information

Nets Hawk Katz
Affiliation: Department of Mathematics, Indiana University, Rawles Hall, 831 East Third St., Bloomington, Indiana 47405

Chun-Yen Shen
Affiliation: Department of Mathematics, Indiana University, Rawles Hall, 831 East Third St., Bloomington, Indiana 47405

DOI: https://doi.org/10.1090/S0002-9939-08-09385-4
Received by editor(s): March 21, 2007
Published electronically: March 10, 2008
Additional Notes: The first author was supported by NSF grant DMS 0432237
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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