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This article is cited in 1 scientific paper (total in 1 paper)
MATHEMATICS
On the problem of describing elements of elliptic fields with a periodic expansion into a continued fraction over quadratic fields
G. V. Fedorov University of Science and Technology "Sirius", Sochi, Russia
Abstract:
For all possible quadratic number fields $K$, we obtain a description of square-free polynomials $f(x)\in K[x]$ of degree 4 such that $\sqrt f$ has a periodic expansion into a continued fraction in the field of formal power series $K((x))$, while the elliptic field $\mathcal L=K(x)(\sqrt f)$ has a fundamental $S$-unit of degree $m$, $4\le m\le 12$, $m\ne11$, where the set $S$ consists of two conjugate valuations defined on the field $\mathcal{L}$ and related to the uniformizer $x$ of the field $K(x)$.
Keywords:
continued fraction, fundamental $S$-unit, elliptic field, divisor class group, cyclotomic polynomials.
Citation:
G. V. Fedorov, “On the problem of describing elements of elliptic fields with a periodic expansion into a continued fraction over quadratic fields”, Dokl. RAN. Math. Inf. Proc. Upr., 505 (2022), 56–62; Dokl. Math., 106:1 (2022), 259–264
Linking options:
https://www.mathnet.ru/eng/danma278 https://www.mathnet.ru/eng/danma/v505/p56
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Abstract page: | 104 | References: | 14 |
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