Platonov, V. P.; Fedorov, G. V. 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 PDFBibTeX XMLCite \textit{V. P. Platonov} and \textit{G. V. Fedorov}, Dokl. Math. 106, Part Suppl. 2, S262--S269 (2022; Zbl 1517.11142); translation from Chebyshevskiĭ Sb. 20, No. 1(69), 248--260 (2019) Full Text: DOI
Platonov, V. P.; Petrunin, M. M.; Shteinikov, Yu. N. On the periodicity problem for the continued fraction expansion of elements of hyperelliptic fields with fundamental \(S\)-units of degree at most 11. (English. Russian original) Zbl 1482.11096 Dokl. Math. 104, No. 2, 258-263 (2021); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 500, 45-51 (2021). MSC: 11J70 11R58 11R27 PDFBibTeX XMLCite \textit{V. P. Platonov} et al., Dokl. Math. 104, No. 2, 258--263 (2021; Zbl 1482.11096); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 500, 45--51 (2021) Full Text: DOI
Platonov, V. P.; Petrunin, M. M.; Shteinikov, Yu. N. On the finiteness of the number of elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\). (English. Russian original) Zbl 1477.11187 Dokl. Math. 100, No. 2, 440-444 (2019); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 488, No. 3, 237-242 (2019). Reviewer: Volker Ziegler (Salzburg) MSC: 11R27 11R58 11J70 11G05 PDFBibTeX XMLCite \textit{V. P. Platonov} et al., Dokl. Math. 100, No. 2, 440--444 (2019; Zbl 1477.11187); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 488, No. 3, 237--242 (2019) Full Text: DOI
Platonov, V. P.; Zhgoon, V. S.; Petrunin, M. M.; Shteinikov, Yu. N. On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\). (English. Russian original) Zbl 1428.11131 Dokl. Math. 98, No. 3, 641-645 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 483, No. 6, 603-608 (2018). Reviewer: Gabriel D. Villa Salvador (México D. F.) MSC: 11J70 11R58 PDFBibTeX XMLCite \textit{V. P. Platonov} et al., Dokl. Math. 98, No. 3, 641--645 (2018; Zbl 1428.11131); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 483, No. 6, 603--608 (2018) Full Text: DOI
Platonov, V. P.; Fedorov, G. V. On the periodicity of continued fractions in hyperelliptic fields. (English. Russian original) Zbl 1418.11109 Dokl. Math. 95, No. 3, 254-258 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 474, No. 5, 540-544 (2017). MSC: 11J70 11A55 11R27 PDFBibTeX XMLCite \textit{V. P. Platonov} and \textit{G. V. Fedorov}, Dokl. Math. 95, No. 3, 254--258 (2017; Zbl 1418.11109); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 474, No. 5, 540--544 (2017) Full Text: DOI
Petrunin, M. M. \(S\)-units and periodicity of square root in hyperelliptic fields. (English. Russian original) Zbl 1406.11042 Dokl. Math. 95, No. 3, 222-225 (2017); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 474, No. 2, 155-158 (2017). MSC: 11F27 11J70 PDFBibTeX XMLCite \textit{M. M. Petrunin}, Dokl. Math. 95, No. 3, 222--225 (2017; Zbl 1406.11042); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 474, No. 2, 155--158 (2017) Full Text: DOI
Platonov, V. P.; Petrunin, M. M. \(S\)-units in hyperelliptic fields and periodicity of continued fractions. (English. Russian original) Zbl 1392.11035 Dokl. Math. 94, No. 2, 532-537 (2016); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 470, No. 3, 260-265 (2016). MSC: 11G16 11A55 11R27 PDFBibTeX XMLCite \textit{V. P. Platonov} and \textit{M. M. Petrunin}, Dokl. Math. 94, No. 2, 532--537 (2016; Zbl 1392.11035); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 470, No. 3, 260--265 (2016) Full Text: DOI