Maximal hyperelliptic curves of genus three

被引：10

作者：

Kodama, Tetsuo ^{[2
]}

Top, Jaap ^{[1
]}

Washio, Tadashi ^{[3
]}

机构：

[1] Univ Groningen, Dept Math, IWI RuG, NL-9747 AG Groningen, Netherlands

[2] Kyushu Univ, Fukuoka 8108560, Japan

[3] Nagasaki Univ, Fac Educ, Dept Math, Nagasaki 8528521, Japan

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2009年 / 15卷 / 03期

关键词：

FINITE-FIELDS; RATIONAL-POINTS;

D O I：

10.1016/j.ffa.2009.02.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This note contains general remarks concerning finite fields over which a so-called maximal, hyperelliptic curve of genus 3 exists. Moreover, the geometry of some specific hyperelliptic curves of genus 3 arising as quotients of Fermat curves, is studied. In particular, this results in a description of the finite fields over which a curve as studied here, is maximal. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：392 / 403

页数：12

共 17 条

[1]

[Anonymous], 2005, ARITHMETIC GEOMETRY

[2]

[Anonymous], 1961, PUBLICATIONS MATH SO

[3] On curves covered by the Hermitian curve [J].

Cossidente, A ;

Korchmáros, G ;

Torres, F .

JOURNAL OF ALGEBRA, 1999, 216 (01) :56-76

[4]

Deuring M., 1941, ABH MATH SEM HAMBURG, V14, P197, DOI 10.1007/BF02940746

[5]

Elkies N., 1999, Math. Sci. Res. Inst. Publ., V35, P51

[6] On subfields of the Hermitian function field [J].

Garcia, A ;

Stichtenoth, H ;

Xing, CP .

COMPOSITIO MATHEMATICA, 2000, 120 (02) :137-170

[7] ON RATIONAL-POINTS OF CURVES OF GENUS-3 OVER FINITE-FIELDS [J].

IBUKIYAMA, T .

TOHOKU MATHEMATICAL JOURNAL, 1993, 45 (03) :311-329

[8] IDEMPOTENT RELATIONS AND FACTORS OF JACOBIANS [J].

KANI, E ;

ROSEN, M .

MATHEMATISCHE ANNALEN, 1989, 284 (02) :307-327

[9] A FAMILY OF HYPERELLIPTIC FUNCTION-FIELDS WITH HASSE-WITT-INVARIANT ZERO [J].

KODAMA, T ;

WASHIO, T .

JOURNAL OF NUMBER THEORY, 1990, 36 (02) :187-200

[10] The maximum or minimum number of rational points on genus three curves over finite fields [J].

Lauter, K ;

Serre, JP .

COMPOSITIO MATHEMATICA, 2002, 134 (01) :87-111

← 1 2 →