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 | Similar Articles | Additional Information

**[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:
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.