A slight improvement to Garaev’s sum product estimate
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- by Nets Hawk Katz and Chun-Yen Shen
- Proc. Amer. Math. Soc. 136 (2008), 2499-2504
- DOI: https://doi.org/10.1090/S0002-9939-08-09385-4
- Published electronically: March 10, 2008
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References
- J. Bourgain, A. A. Glibichuk, and S. V. Konyagin, Estimates for the number of sums and products and for exponential sums in fields of prime order, J. London Math. Soc. (2) 73 (2006), no. 2, 380–398. MR 2225493, DOI 10.1112/S0024610706022721
- J. Bourgain, N. Katz, and T. Tao, A sum-product estimate in finite fields, and applications, Geom. Funct. Anal. 14 (2004), no. 1, 27–57. MR 2053599, DOI 10.1007/s00039-004-0451-1 [G1]G1 Garaev, M.Z., An explicit sum-product estimate in $\mathbb {F}_{p}$, preprint, http://arxiv.org/ abs/math/0702780. [G2]G2 Garaev, M.Z., The sum product estimate for large subsets of prime orders, preprint, http://arxiv.org/abs/0706.0702. [GK]GK Glibichuk, A.A., and Konyagin, S.V., Additive properties of product sets in fields of prime order, preprint.
- József Solymosi, On the number of sums and products, Bull. London Math. Soc. 37 (2005), no. 4, 491–494. MR 2143727, DOI 10.1112/S0024609305004261
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Bibliographic Information
- Nets Hawk Katz
- Affiliation: Department of Mathematics, Indiana University, Rawles Hall, 831 East Third St., Bloomington, Indiana 47405
- MR Author ID: 610432
- Chun-Yen Shen
- Affiliation: Department of Mathematics, Indiana University, Rawles Hall, 831 East Third St., Bloomington, Indiana 47405
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2390519