On the sum product estimates and two variables expanders
Shen, Chun-Yen (Indiana University (Estats Units d'Amèrica). Department of Mathematics)

Date:	2010
Abstract:	Let Fp be the finite field of a prime order p. Let F: Fp x Fp --> Fp be a function defined by F(x, y) = x(f(x) + by), where b ∈ F*/p and f: Fp → Fp is any function. We prove that if A ⊂ Fp and │A│ < p1/2 then │A + A│+│F(A,A) │⪆│A│13/12. Taking f = 0 and b = 1, we get the well-known sum-product theorem by Bourgain, Katz and Tao, and Bourgain, Glibichuk and Konyagin, and also improve the previous known exponent from 14/13 to 13/12.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Sums ; Products ; Expanders
Published in:	Publicacions matemàtiques, V. 54 n. 1 (2010) p. 149-157, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/154821
DOI: 10.5565/PUBLMAT_54110_08

9 p, 134.7 KB

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