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Asymptotic behavior of period lengths of continued fractions in a hyperelliptic fieldстатья
- Авторы: Platonov V.P., Fedorov G.V.
- Журнал: Izvestiya. Mathematics
- Том: 89
- Номер: 6
- Год издания: 2025
- Издательство: American Mathematical Society
- Местоположение издательства: United States
- Аннотация: The problem of unbounded lengths of periods and quasi-periods of functional continued fractions constructed in the field of formal power series K((1/x)), for elements from a given hyperelliptic field L defined over a field K of characteristic different from 2 is solved. It is proved that if in the hyperelliptic field L there is an element with a periodic expansion into a functional continued fraction, then in the field L there is an element for which the length of the period of the continued fraction is greater than any predetermined number. As a consequence, a result is obtained on the unbounded lengths of periods in sequences of powers of incomplete quotients corresponding to the expansion into a functional continued fraction of elements of the field L.
- Добавил в систему: Федоров Глеб Владимирович