Doklady Akademii Nauk
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Dokl. Akad. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Doklady Akademii Nauk, 2016, Volume 470, Number 3, Pages 260–265
DOI: https://doi.org/10.7868/S0869565216270074
(Mi dan25565)
 

This article is cited in 20 scientific papers (total in 21 papers)

SS-units in hyperelliptic fields and periodicity of continued fractions

V. P. Platonov, M. M. Petrunin

Scientific Research Institute of System Development, Russian Academy of Sciences, Nakhimovskii pr. 36, korp. 1, Moscow, 117218 Russia
Citations (21)
Funding agency Grant number
Russian Science Foundation 16-11-10111
This work was supported by the Russian Science Foundation, project no. 16-11-10111.
Received: 02.06.2016
English version:
Doklady Mathematics, 2016, Volume 94, Issue 2, Pages 532–537
DOI: https://doi.org/10.1134/S1064562416050148
Bibliographic databases:
Document Type: Article
Language: Russian
Linking options:
  • https://www.mathnet.ru/eng/dan25565
  • This publication is cited in the following 21 articles:
    1. V. P. Platonov, V. S. Zhgoon, M. M. Petrunin, “On the problem of periodicity of continued fraction expansions of $\sqrt{f}$ for cubic polynomials $f$ over algebraic number fields”, Sb. Math., 213:3 (2022), 412–442  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. 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
    3. 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
    4. 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
    5. 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
    6. 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
    7. 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
    8. 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
    9. 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
    10. 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
    11. 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
    12. 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
    13. Kuznetsov Yu.V., Shteinikov Yu.N., “O nekotorykh usloviyakh na nepolnye chastnye nepreryvnykh drobei, svyazannykh s giperellipticheskimi polyami i S-edinitsami”, Trudy NIISI RAN, 7:4 (2018), 184  crossref
    14. 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
    15. 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
    16. Petrunin M. M., “Kvaziperiodicheskie, no ne periodicheskie funktsionalnye nepreryvnye drobi malykh kvaziperiodov”, Trudy NIISI RAN, 7:3 (2017), 14  crossref
    17. M. Petrunin, “S-EDINITsY I PERIODIChNOST KVADRATNOGO KORNYa V GIPERELLIPTIChESKIKh POLYaKh”, Doklady Akademii nauk, 2017, no. 2, 155  crossref
    18. V. P. Platonov, G. V. Fedorov, “On the periodicity of continued fractions in elliptic fields”, Dokl. Math., 96:1 (2017), 332–335  mathnet  mathnet  crossref  crossref  isi  scopus
    19. V. P. Platonov, G. V. Fedorov, “On the periodicity of continued fractions in hyperelliptic fields”, Dokl. Math., 95:3 (2017), 254–258  mathnet  mathnet  crossref  crossref  isi  scopus
    20. M. M. Petrunin, “S-units and periodicity of square root in hyperelliptic fields”, Dokl. Math., 95:3 (2017), 222  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:175
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025