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arXiv · 0809.4931

Multi-valued hyperelliptic continued fractions of generalized Halphen type

Vladimir Dragovic
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Abstract

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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Vladimir Dragovic. 2008-09-29. Multi-valued hyperelliptic continued fractions of generalized Halphen type. https://arxiv.org/abs/0809.4931

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