Conditional expanding bounds for two-variable functions over finite valuation rings

被引：5

作者：

Le Quang Ham ^{[1
]}

Pham Van Thang ^{[2
]}

Le Anh Vinh ^{[3
]}

机构：

[1] Vietnam Natl Univ Hanoi, Univ Sci, Hanoi, Vietnam

[2] Ecole Polytech Fed Lausanne, Lausanne, Switzerland

[3] Vietnam Natl Univ Hanoi, Univ Educ, Hanoi, Vietnam

来源：

EUROPEAN JOURNAL OF COMBINATORICS | 2017年 / 60卷

基金：

瑞士国家科学基金会;

关键词：

SUM-PRODUCT ESTIMATE; FIELDS;

D O I：

10.1016/j.ejc.2016.09.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we use methods from spectral graph theory to obtain some results on the sum-product problem over finite valuation rings R of order q(r) which generalize recent results given by Hegyvari and Hennecart (2013). 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 R* with vertical bar A vertical bar = vertical bar B vertical bar = q(alpha), then max {vertical bar f(A, B)vertical bar, vertical bar g(A, B)vertical bar} >> vertical bar A vertical bar(1+Delta(alpha)), for some Delta(alpha) > 0. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：114 / 123

页数：10

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