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Uspekhi Mat. Nauk, 2016, Volume 71, Issue 5(431), Pages 181–182 (Mi umn9737)  

This article is cited in 14 scientific papers (total in 15 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

$S$-Units and periodicity in quadratic function fields

V. P. Platonov, M. M. Petrunin

Scientific Research Institute for System Analysis of the Russian Academy of Sciences

Funding Agency Grant Number
Russian Science Foundation 16-11-10111
This research was supported by the Russian Science Foundation (grant no. 16-11-10111).


DOI: https://doi.org/10.4213/rm9737

Full text: PDF file (319 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2016, 71:5, 973–975

Bibliographic databases:

MSC: Primary 11R11; Secondary 11G16, 11J70, 11R27
Presented: В. М. Бухштабер
Accepted: 20.09.2016

Citation: V. P. Platonov, M. M. Petrunin, “$S$-Units and periodicity in quadratic function fields”, Uspekhi Mat. Nauk, 71:5(431) (2016), 181–182; Russian Math. Surveys, 71:5 (2016), 973–975

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/umn/v71/i5/p181

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Platonov, G. V. Fedorov, “On the periodicity of continued fractions in elliptic fields”, Dokl. Math., 96:1 (2017), 332–335  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    2. M. M. Petrunin, “$S$-units and periodicity of square root in hyperelliptic fields”, Dokl. Math., 95:3 (2017), 222–225  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    3. V. P. Platonov, G. V. Fedorov, “On the periodicity of continued fractions in hyperelliptic fields”, Dokl. Math., 95:3 (2017), 254–258  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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
    5. 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  adsnasa  isi  elib
    6. 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
    7. V. P. Platonov, V. S. Zhgoon, M. M. Petrunin, 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  crossref  crossref  zmath  isi  elib
    8. 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
    9. V. P. Platonov, G. V. Fedorov, “Kriterii periodichnosti nepreryvnykh drobei klyuchevykh elementov giperellipticheskikh polei”, Chebyshevskii sb., 20:1 (2019), 248–260  mathnet  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. 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  isi  elib
    12. 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  isi
    13. 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  isi  elib
    14. 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
    15. 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
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