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On the classification problem for polynomials f with a periodic continued fraction expansion of √f in hyperelliptic fieldsстатья
Дата последнего поиска статьи во внешних источниках: 8 декабря 2021 г.
- Авторы: Platonov V.P., Fedorov G.V.
- Журнал: Izvestiya. Mathematics
- Том: 85
- Номер: 5
- Год издания: 2021
- Издательство: American Mathematical Society
- Местоположение издательства: United States
- Первая страница: 972
- Последняя страница: 1007
- DOI: 10.4213/im9098
- Аннотация: The classical problem of the periodicity of continued fractions for elements of hyperelliptic fields has a long and deep history. This problem has up to now been far from completely solved. A surprising result was obtained in [1] for quadratic extensions defined by cubic polynomials with coefficients in the field Q of rational numbers: except for trivial cases there are only three (up to equivalence) cubic polynomials over Q whose square root has a periodic continued fraction expansion in the field Q((x)) of formal power series. In view of the results in [1], we completely solve the classification problem for polynomials f with periodic continued fraction expansion of √f in elliptic fields with the field of rational numbers as the field of constants.
- Добавил в систему: Федоров Глеб Владимирович