A Szemeredi-Trotter type theorem, sum-product estimates in finite quasifields, and related results

被引：3

作者：

Thang Pham ^{[1
]}

Tait, Michael ^{[2
]}

Timmons, Craig ^{[3
]}

Le Anh Vinh ^{[4
]}

机构：

[1] Ecole Polytech Fed Lausanne, Lausanne, Switzerland

[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

[3] Calif State Univ Sacramento, Dept Math & Stat, Sacramento, CA 95819 USA

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

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2017年 / 147卷

基金：

美国国家科学基金会; 瑞士国家科学基金会;

关键词：

Szemeredi-Trotter theorem; Quasifield; Sum-product estimate; EQUATIONS; FIELDS; SETS;

D O I：

10.1016/j.jcta.2016.11.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a Szemeredi-Trotter type theorem and a sum product estimate in the setting of finite quasifields. These estimates generalize results of the fourth author, of Garaev, and of Vu. We generalize results of Gyarmati and Sarkozy on the solvability of the equations a + b = cd and ab + 1 = cd over a finite field. Other analogous results that are known to hold in finite fields are generalized to finite quasifields. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：55 / 74

页数：20

共 4 条

[1] Erdos-Renyi graph, Szemeredi-Trotter type theorem, and sum-product estimates over finite rings
Pham Van Thang
Le Anh Vinh
FORUM MATHEMATICUM, 2015, 27 (01) : 331 - 342
[2] Product graphs, sum-product graphs and sum-product estimates over finite rings
Le Anh Vinh
FORUM MATHEMATICUM, 2015, 27 (03) : 1639 - 1655
[3] New sum-product type estimates over finite fields
Roche-Newton, Oliver
Rudnev, Misha
Shkredov, Ilya D.
ADVANCES IN MATHEMATICS, 2016, 293 : 589 - 605
[4] SUM-PRODUCT ESTIMATES AND MULTIPLICATIVE ORDERS OF γ AND γ + γ-1 IN FINITE FIELDS
Shparlinski, Igor
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2012, 85 (03) : 505 - 508

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