广义Hücken型多值超椭圆连分数
Multi-valued hyperelliptic continued fractions of generalized Halphen type
摘要：
本文介绍并研究了连分数的Hüssen理论的更高一般推广。我们开始的基本概念是超椭圆Haplhen（HH）元素$$\frac{\sqrt{X_{2g+2}}-\sqrt{Y_{2g+2}}}{x-y},$$取决于参数$y$，其中$X_{2g+2}$是次数为$2g+2$和$Y_{2g+2}=X_{2g+2}(y)$的多项式。我们研究了规则和不规则HH元素。它们的连分数发展以及这种发展的一些基本性质：奇偶对称性和周期性。
英文摘要：
We introduce and study higher genera generalizations of the Halphen theory of continued fractions. The basic notion we start with is hyperelliptic Haplhen (HH) element $$\frac{\sqrt{X_{2g+2}}-\sqrt{Y_{2g+2}}}{x-y},$$ depending on parameter $y$, where $X_{2g+2}$ is a polynomial of degree $2g+2$ and $Y_{2g+2}=X_{2g+2}(y)$. We study regular and irregular HH elements. their continued fraction development and some basic properties of such development: even and odd symmetry and periodicity.
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