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Doklady Akademii Nauk, 2017, Volume 475, Number 2, Pages 133–136
DOI: https://doi.org/10.7868/S0869565217020037
(Mi dan26108)
 

This article is cited in 15 scientific papers (total in 16 papers)

On the periodicity of continued fractions in elliptic fields

V. P. Platonovab, G. V. Fedorovca

a Scientific Research Institute for System Analysis of the Russian Academy of Sciences, Moscow
b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
c Lomonosov Moscow State University
Citations (16)
Funding agency Grant number
Russian Science Foundation 16-11-10111
Работа выполнена при поддержке Российского научного фонда (грант 16-11-10111).
Received: 30.03.2017
English version:
Doklady Mathematics, 2017, Volume 96, Issue 1, Pages 332–335
DOI: https://doi.org/10.1134/S1064562417040068
Bibliographic databases:
Document Type: Article
Language: Russian
Linking options:
  • https://www.mathnet.ru/eng/dan26108
  • This publication is cited in the following 16 articles:
    1. G.V. Fedorov, “On the sequences of polynomials $f$ with a periodic continued fraction expansion $\sqrt{f}$”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 79:2 (2024), 98–102  mathnet  mathnet  crossref  crossref
    2. G. V. Fedorov, “Continued Fractions and the Classification Problem for Elliptic Fields Over Quadratic Fields of Constants”, Math. Notes, 114:6 (2023), 1195–1211  mathnet  crossref  crossref
    3. V. P. Platonov, G. V. Fedorov, “On the classification problem for polynomials $f$ with a periodic continued fraction expansion of $\sqrt{f}$ in hyperelliptic fields”, Izv. Math., 85:5 (2021), 972–1007  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. G. V. Fedorov, “On $S$-units for valuations of the second degree in hyperelliptic fields”, Izv. Math., 84:2 (2020), 392–435  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. S. I. Adian, V. M. Buchstaber, E. I. Zelmanov, S. V. Kislyakov, V. V. Kozlov, Yu. V. Matiyasevich, S. P. Novikov, D. O. Orlov, A. N. Parshin, V. L. Popov, D. V. Treschev, “Vladimir Petrovich Platonov (on his 80th birthday)”, Russian Math. Surveys, 75:2 (2020), 387–391  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    6. V. P. Platonov, G. V. Fedorov, “On the problem of classification of periodic continued fractions in hyperelliptic fields”, Russian Math. Surveys, 75:4 (2020), 785–787  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. V. P. Platonov, M. M. Petrunin, Yu. N. Shteinikov, “Periodicheskie elementy $\sqrt{f}$ v ellipticheskikh polyakh s polem konstant nulevoi kharakteristiki”, Chebyshevskii sb., 21:1 (2020), 273–296  mathnet  crossref  mathscinet
    8. G. V. Fedorov, “O semeistvakh giperellipticheskikh krivykh nad polem ratsionalnykh chisel, yakobiany kotorykh soderzhat tochki krucheniya dannykh poryadkov”, Chebyshevskii sb., 21:1 (2020), 322–340  mathnet  crossref
    9. V. P. Platonov, G. V. Fedorov, “The criterion of periodicity of continued fractions of key elements in hyperelliptic fields”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 262–269  mathnet  crossref  crossref
    10. G. V. Fedorov, “Ob ogranichennosti dlin periodov nepreryvnykh drobei klyuchevykh elementov giperellipticheskikh polei nad polem ratsionalnykh chisel”, Chebyshevskii sb., 20:4 (2019), 357–370  mathnet  crossref
    11. V. P. Platonov, G. V. Fedorov, “On $S$-units for linear valuations and the periodicity of continued fractions of generalized type in hyperelliptic fields”, Dokl. Math., 99:3 (2019), 277–281  mathnet  mathnet  crossref  crossref  isi  scopus
    12. V. P. Platonov, G. V. Fedorov, “On the problem of periodicity of continued fractions in hyperelliptic fields”, Sb. Math., 209:4 (2018), 519–559  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. V. P. Platonov, M. M. Petrunin, “Groups of $S$-units and the problem of periodicity of continued fractions in hyperelliptic fields”, Proc. Steklov Inst. Math., 302 (2018), 336–357  mathnet  crossref  crossref  mathscinet  isi  elib
    14. G. V. Fedorov, “Periodicheskie nepreryvnye drobi i $S$-edinitsy s normirovaniyami vtoroi stepeni v giperellipticheskikh polyakh”, Chebyshevskii sb., 19:3 (2018), 282–297  mathnet  crossref  elib
    15. V. P. Platonov, M. M. Petrunin, V. S. Zhgoon, Yu. N. Shteinikov, “On the Finiteness of Hyperelliptic Fields with Special Properties and Periodic Expansion of $\sqrt f$”, Dokl. Math., 98:3 (2018), 641–645  mathnet  mathnet  crossref  crossref  isi  scopus
    16. Yu. V. Kuznetsov, Yu. N. Shteinikov, “O nekotorykh svoistvakh nepreryvnykh periodicheskikh drobei s nebolshoi dlinoi perioda, svyazannykh s giperellipticheskimi polyami i $S$-edinitsami”, Chebyshevskii sb., 18:4 (2017), 261–268  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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