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A slight improvement to Garaev's sum product estimate
Author(s):
Nets
Hawk
Katz;
Chun-Yen
Shen
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2499-2504.
MSC (2000):
Primary 42B25;
Secondary 60K35
Posted:
March 10, 2008
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Additional information
References:
-
- [BGK]
- Bourgain, J., Glibichuk, A.A., and Konyagin, S.V., Estimates for the number of sums and products and for exponential sums in fields of prime order, J. London Math. Soc. (2) 73 (2006), 380-398. MR 2225493 (2007e:11092)
- [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
 , 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:
10.1090/S0002-9939-08-09385-4
PII:
S 0002-9939(08)09385-4
Received by editor(s):
March 21, 2007
Posted:
March 10, 2008
Additional Notes:
The first author was supported by NSF grant DMS 0432237
Communicated by:
Michael T. Lacey
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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