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

Published electronically:
March 10, 2008

MathSciNet review:
2390519

Full-text PDF Free Access

References | Similar Articles | Additional Information

**[BGK]**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**, 10.1112/S0024610706022721**[BKT]**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**, 10.1007/s00039-004-0451-1**[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]**József Solymosi,*On the number of sums and products*, Bull. London Math. Soc.**37**(2005), no. 4, 491–494. MR**2143727**, 10.1112/S0024609305004261**[TV]**Terence Tao and Van Vu,*Additive combinatorics*, Cambridge Studies in Advanced Mathematics, vol. 105, Cambridge University Press, Cambridge, 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:
http://dx.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.