The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications

被引：1

作者：

Ayano, T. ^{[1
]}

Buchstaber, V. M. ^{[2
]}

机构：

[1] Natl Res Univ Higher Sch Econ, Fac Math, Moscow, Russia

[2] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

来源：

FUNCTIONAL ANALYSIS AND ITS APPLICATIONS | 2017年 / 51卷 / 03期

关键词：

Abelian functions; hyperelliptic sigma functions; polynomial dynamical systems; commuting vector fields; symmetric products of algebraic curves; ABELIAN FUNCTIONS; EXPRESSIONS;

D O I：

10.1007/s10688-017-0181-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 is described in terms of the gradient of its sigma function. As an application, solutions of the corresponding families of polynomial dynamical systems in C-4 with two polynomial integrals are constructed. These systems were introduced by Buchstaber and Mikhailov on the basis of commuting vector fields on the symmetric square of algebraic curves.

引用

页码：162 / 176

页数：15

共 18 条

[1] The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications
T. Ayano
V. M. Buchstaber
Functional Analysis and Its Applications, 2017, 51 : 162 - 176
[2] Construction of Two Parametric Deformation of KdV-Hierarchy and Solution in Terms of Meromorphic Functions on the Sigma Divisor of a Hyperelliptic Curve of Genus 3
Ayano, Takanori
Buchstaber, Victor M.
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2019, 15
[3] Dispersionless Hirota Equations and the Genus 3 Hyperelliptic Divisor
Fabien Cléry
Evgeny V. Ferapontov
Communications in Mathematical Physics, 2020, 376 : 1397 - 1412
[4] Dispersionless Hirota Equations and the Genus 3 Hyperelliptic Divisor
Clery, Fabien
Ferapontov, Evgeny, V
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2020, 376 (02) : 1397 - 1412
[5] A complete divisor class halving algorithm for hyperelliptic curve cryptosystems of genus two
Kitamura, I
Katagi, M
Takagi, T
INFORMATION SECURITY AND PRIVACY, PROCEEDINGS, 2005, 3574 : 146 - 157
[6] On hyperelliptic abelian functions of genus 3
Nakayashiki, Atsushi
JOURNAL OF GEOMETRY AND PHYSICS, 2011, 61 (06) : 961 - 985
[7] Differentiation of genus 3 hyperelliptic functions
Bunkova, Elena Yu.
EUROPEAN JOURNAL OF MATHEMATICS, 2018, 4 (01) : 93 - 112
[8] Performance Study of genus 3 Hyperelliptic Curve Cryptosystem
Gupta, Daya
De, Asok
Chatterjee, Kakali
JOURNAL OF INFORMATION PROCESSING SYSTEMS, 2012, 8 (01): : 145 - 158
[9] Simultaneous divisor class addition-subtraction algorithm and its applications to hyperelliptic curve cryptosystem
Fan, XX
Wang, YM
19th International Conference on Advanced Information Networking and Applications, Vol 1, Proceedings: AINA 2005, 2005, : 978 - 983
[10] Efficiently computable endomorphism for genus 3 hyperelliptic curve cryptosystems
Feng, Jun
Wang, Xueming
Sun, Hong
INFORMATION PROCESSING LETTERS, 2013, 113 (12) : 405 - 408

← 1 2 →