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On the Periodicity of Continued Fractions in Hyperelliptic Fieldsстатья
- Автор: Fedorov G.V.
- Сборник: Advances in Dynamical Systems and Control
- Редактор: Садовничий Виктор Антонович
- Серия: Studies in Systems, Decision and Control
- Том: 69
- Глава в коллективной монографии
- Год издания: 2016
- Место издания: Springer Switzerland
- Первая страница: 141
- Последняя страница: 157
- DOI: 10.1007/978-3-319-40673-2
- Аннотация: Let L be a function field of a hyperelliptic curve defined over an arbitrary field characteristic different from 2. We construct an arithmetic of continued fractions of an arbitrary quadratic irrationality in field of formal power series with respect to linear finite valuation. The set of infinite valuation and finite linear valuation of L is denoted by S. As an application, we have found a relationship between the issue of the existence of nontrivial S-units in L and periodicity of continued fractions of some key elements of L.
- Добавил в систему: Федоров Глеб Владимирович