Sziklai's conjecture on the number of points of a plane curve over a finite field III

被引：23

作者：

Homma, Masaaki ^{[1
]}

Kim, Seon Jeong ^{[2
,3
]}

机构：

[1] Kanagawa Univ, Dept Math, Yokohama, Kanagawa 2218686, Japan

[2] Gyeongsang Natl Univ, Dept Math, Jinju 660701, South Korea

[3] Gyeongsang Natl Univ, RINS, Jinju 660701, South Korea

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2010年 / 16卷 / 05期

关键词：

Plane curve; Finite field; Rational point; Frobenius nonclassical curve;

D O I：

10.1016/j.ffa.2010.05.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We manage an upper bound for the number of rational points of a Frobenius nonclassical plane curve over a finite field. Together with previous results, the modified Sziklai conjecture is settled affirmatively. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：315 / 319

页数：5

共 9 条

[1] FROBENIUS NONCLASSICAL CURVES [J].

HEFEZ, A ;

VOLOCH, JF .

ARCHIV DER MATHEMATIK, 1990, 54 (03) :263-273

[2] CORRECTION [J].

HEFEZ, A .

ARCHIV DER MATHEMATIK, 1991, 57 (04) :416-416

[3]

Hirschfeld J.W.P., 2008, Princeton Series in Applied Mathematics

[4] On the number of solutions of an equation over a finite field [J].

Hirschfeld, JWP ;

Korchmaros, G .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2001, 33 :16-24

[5]

HOMMA M, 2010, DETERMINATION OPTIMA

[6]

HOMMA M, 2010, CONT MATH IN PRESS, V518

[7] Around Sziklai's conjecture on the number of points of a plane curve over a finite field [J].

Homma, Masaaki ;

Kim, Seon Jeong .

FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (04) :468-474

[8]

STOHR KO, 1986, P LOND MATH SOC, V52, P1

[9] A bound on the number of points of a plane curve [J].

Sziklai, Peter .

FINITE FIELDS AND THEIR APPLICATIONS, 2008, 14 (01) :41-43

← 1 →