In this paper we propose a new effective approach to the problem of finding and constructing non-trivial ##IMG## [http://ej.iop.org/images/1064-5632/84/2/392/toc_IZV_84_2_392ieqn1.gif] {$S$} -units of a hyperelliptic field ##IMG## [http://ej.iop.org/images/1064-5632/84/2/392/IZV_84_2_392ieqn2.gif] {$L$} for a set ##IMG## [http://ej.iop.org/images/1064-5632/84/2/392/IZV_84_2_392ieqn3.gif] {$S=S_h$} consisting of two conjugate valuations of the second degree. The results obtained are based on a deep connection between the problem of torsion in the Jacobians of hyperelliptic curves and the quasiperiodicity of continued ##IMG## [http://ej.iop.org/images/1064-5632/84/2/392/IZV_84_2_392ieqn4.gif] {$h$} -fractions, that is, generalized functional continued fractions of special form constructed with respect to a valuation of the second degree. We find algorithms for searching for fundamental ##IMG##

中文翻译：

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在## IMG ##上[http://ej.iop.org/images/1064-5632/84/2/392/toc_IZV_84_2_392ieqn1.gif] {$ S $}-表示超椭圆场中第二度的估值单位

在本文中，我们针对发现和构造非平凡的## IMG ##问题提出了一种新的有效方法[http://ej.iop.org/images/1064-5632/84/2/392/toc_IZV_84_2_392ieqn1.gif ] {$ S $}-超椭圆字段的单位## IMG ## [http://ej.iop.org/images/1064-5632/84/2/392/IZV_84_2_392ieqn2.gif] {$ L $}为一组## IMG ## [http://ej.iop.org/images/1064-5632/84/2/392/IZV_84_2_392ieqn3.gif] {$ S = S_h $}，包含两个第二度的共轭估值。获得的结果基于超椭圆​​曲线的雅可比曲线中的扭转问题与连续的## IMG ##的拟周期性之间的深层联系[http://ej.iop.org/images/1064-5632/84/2 /392/IZV_84_2_392ieqn4.gif] {$ h $}-分数，即，相对于二阶评估而言，构造的特殊形式的广义函数连续分数。