Conditional expanding bounds for two-variable functions over arbitrary fields

JOURNAL OF NUMBER THEORY

卷:186

Article

Mojarrad, Hossein Nassajian¹  Thang Pham¹ 

[1] Ecole Polytech Fed Lausanne, Dept Math, Lausanne, Switzerland

关键词: Sum-product estimates;    Incidence geometry;    Expanders;   

DOI  :  10.1016/j.jnt.2017.09.020

来源: Elsevier

【 摘 要 】

In this paper, we prove some results on the sum-product problem over arbitrary fields which improve and generalize results given by Hogyvari and Hennecart [5]. More precisely, we prove that, for related pairs of two-variable functions f (x, y) and g(x,y), if A and B are two sets in an arbitrary field IF with vertical bar A vertical bar = vertical bar B vertical bar, then max {vertical bar f(A,B)vertical bar, vertical bar g(A,B)vertical bar} >> vertical bar A vertical bar(1+c) for some c > 0. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free