Systems of uniformization equations and hyperelliptic integrals
Systems of uniformization equations and hyperelliptic integrals
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均匀化方程组和超椭圆积分
DOI：
10.1007/s10958-011-0333-7
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
J. Sekiguchi
中科院分区：
文献类型：
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作者：
Sekiguchi;Jiro;Yasushi Yamashita;南 範彦;A. G. Aleksandrov and J. Sekiguchi;小池敏司;Yasushi Yamashita;南 範彦;Satoshi Koike;J. Sekiguchi
本文的目的是研究关于Saito自由因子的单值化方程组，其解用超椭圆积分表示。有两个这样的除数。它们都是由加权齐次多项式定义的三维仿射空间中的超曲面。一个是由2（2n+1）阶二面体群的判别式构造的。另一个是H3型反射群的判别式。在前一种情况下，我们除了用超椭圆积分表示的解之外，还用高斯超几何函数构造基本解。
The purpose of this paper is to study systems of uniformization equations with respect to Saito free divisors which have solutions expressed in terms of hyperelliptic integrals. There are two such divisors. Both are hypersurfaces in a three-dimensional affine space defined by weighted homogeneous polynomials. One is constructed by the discriminant of a dihedral group of order 2(2n+1). The other is the discriminant of the reflection group of typeH3. In the former case, we construct fundamental solutions by Gaussian hypergeometric functions in addition to a solution expressed by a hyperelliptic integral.