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Found 380 Documents (Results 1–100)

Periodicity criterion for continued fractions of key elements in hyperelliptic fields. (English. Russian original) Zbl 1517.11142

Dokl. Math. 106, Part Suppl. 2, S262-S269 (2022); translation from Chebyshevskiĭ Sb. 20, No. 1(69), 248-260 (2019).
MSC:  11R58 11G16 11J70
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On the problem of describing elements of elliptic fields with a periodic expansion into a continued fraction over quadratic fields. (English. Russian original) Zbl 1503.11102

Dokl. Math. 106, No. 1, 259-264 (2022); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 505, 56-62 (2022).
MSC:  11J70 11R58 11R27
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On fundamental \(S\)-units and continued fractions constructed in hyperelliptic fields using two linear valuations. (English. Russian original) Zbl 1475.11133

Dokl. Math. 103, No. 3, 151-156 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 498, 65-70 (2021).
MSC:  11J70 11R58 11R27
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Diophantine equation generated by the maximal subfield of a circular field. (English. Russian original) Zbl 1456.11203

Russ. Math. 64, No. 7, 38-47 (2020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 7, 45-55 (2020).
MSC:  11R04 11R16 11D25
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Divisibility of class number of a real cubic or quadratic field and its fundamental unit. (English) Zbl 1444.11221

Chakraborty, Kalyan (ed.) et al., Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4–7, 2017. Singapore: Springer. 67-72 (2020).
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The criterion of periodicity of continued fractions of key elements in hyperelliptic fields. (Russian. English summary) Zbl 1439.11286

Chebyshevskiĭ Sb. 20, No. 1(69), 248-260 (2019); translation in Dokl. Math. 106, Suppl. 2, S262-S269 (2022).
MSC:  11R58 11G16 11J70
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Fundamental units for orders of unit rank 1 and generated by a unit. (English) Zbl 1411.11107

Gładki, Paweł (ed.) et al., Algebra, logic and number theory. Proceedings of the 3rd joint conferences on algebra, logic and number theory, Bȩdlewo, Poland, June 8–13, 2014. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-31-7/pbk). Banach Center Publications 108, 173-189 (2016).
MSC:  11R27 11R54 11R16
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Group ring groups. Volume 2: Structure theorems of unit groups. (English) Zbl 1338.16002

De Gruyter Textbook. Berlin: De Gruyter (ISBN 978-3-11-041149-2/pbk; 978-3-11-041150-8/ebook). x, 217 p. (2016).
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Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field. (English. Russian original) Zbl 1305.11096

Russ. Math. Surv. 69, No. 1, 1-34 (2014); translation from Usp. Mat. Nauk 69, No. 1, 3-38 (2014).
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Searching discriminants with large fundamental units via continued fraction expansion. (English) Zbl 1307.11012

Amou, Masaaki (ed.) et al., Diophantine analysis and related fields 2011, DARF–2011. Proceedings of the conference, Musashino, Tokyo, Japan, March 3–5, 2011. Melville, NY: American Institute of Physics (AIP) (ISBN 978-0-7354-0947-7/pbk). AIP Conference Proceedings 1385, 38-41 (2011).
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A new local-global principle for quadratic function fields. (English. Russian original) Zbl 1244.11093

Dokl. Math. 82, No. 1, 531-534 (2010); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 433, No. 2, 154-157 (2010).
MSC:  11R58 11R27
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