On fundamental S-units and continued fractions, constructed in hyperelliptic fields by two linear valuationsстатья
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Дата последнего поиска статьи во внешних источниках: 23 сентября 2021 г.
Аннотация:In this paper, for the elements of hyperelliptic fields, the theory of functional continued fractions of generalized type associated with two linear valuations is formulated for the first time. For an arbitrary element of the hyperelliptic field, the continued fraction of the generalized type converges to this element for each of the two selected linear valuations of the hyperelliptic field. Denote by S the set consisting of these two linear valuations. We find equivalent conditions describing the relationship between the condition of a continued fraction of generalized type, the existence of a fundamental S-unit, and the existence of a class of divisors of finite order in the divisor class group of a hyperelliptic field. The last condition is equivalent to the existence of a torsion point in the Jacobian of a hyperelliptic curve. These results complete