On S-units for linear valuations and periodicity of continued fractions of generalized type in hyperelliptic fieldsстатья
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Дата последнего поиска статьи во внешних источниках: 15 августа 2019 г.
Аннотация:An equivalence theorem is proved for the following conditions: the periodicity of continued fractions
of generalized type for key elements of hyperelliptic field , the existence of nontrivial S-units in L for sets consisting two valuations of degree one, and the existence of a torsion of certain type in the Jacobian variety associated with hyperelliptic field L. In practice, this theorem allows using continued fractions of generalized type to effectively search for fundamental S-units of hyperelliptic fields. We give an example of the hyperelliptic field of genus 3, which shows all three equivalent conditions in the indicated theorem.