The sum-product estimate for large subsets of prime fields
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- by M. Z. Garaev PDF
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Abstract:
Let $\mathbb {F}_p$ be the field of prime order $p.$ It is known that for any integer $N\in [1,p]$ one can construct a subset $A\subset \mathbb {F}_p$ with $|A|= N$ such that \[ \max \{|A+A|, |AA|\}\ll p^{1/2}|A|^{1/2}. \] One of the results of the present paper implies that if $A\subset \mathbb {F}_p$ with $|A|>p^{2/3},$ then \[ \max \{|A+A|, |AA|\}\gg p^{1/2}|A|^{1/2}. \]References
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Additional Information
- M. Z. Garaev
- Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Campus Morelia, Apartado Postal 61-3 (Xangari), C.P. 58089, Morelia, Michoacán, México
- MR Author ID: 632163
- Email: garaev@matmor.unam.mx
- Received by editor(s): June 26, 2007
- Published electronically: April 14, 2008
- Communicated by: Ken Ono
- © 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), 2735-2739
- MSC (2000): Primary 11B75, 11T23
- DOI: https://doi.org/10.1090/S0002-9939-08-09386-6
- MathSciNet review: 2399035