The function of a cyclic trigonal curve of genus three

被引：0

作者：

Matsutani, Shigeki ^{[1
]}

Previato, Emma ^{[2
]}

机构：

[1] Natl Inst Technol, Div Ind Math, Sasebo Coll, Nagasaki 8571193, Japan

[2] Boston Univ, Dept Math & Stat, Boston, MA 02215 USA

来源：

COLLECTANEA MATHEMATICA | 2015年 / 66卷 / 03期

关键词：

HYPERELLIPTIC SOLUTIONS; ABELIAN FUNCTIONS; JACOBI INVERSION; FORMULAS; EQUATIONS; STRATA; SYSTEM; FLOWS; Y(R);

D O I：

10.1007/s13348-015-0138-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A cyclic trigonal curve of genus three is a Galois cover of , therefore can be written as a smooth plane curve with equation . Following Weierstrass for the hyperelliptic case, we define an "" function for this curve and , , for each one of three particular covers of the Jacobian of the curve, and for a finite branchpoint . This generalization of the Jacobi , , functions satisfies the relation: Sigma(4)(r=1) Pi(2)(c=0) al(r)((c)) (u)/f'(b(r)) = 1 which generalizes . We also show that this can be viewed as a special case of the Frobenius theta identity.

引用

页码：311 / 349

页数：39

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