RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. Akad. Nauk SSSR Ser. Mat., 1980, Volume 44, Issue 1, Pages 24–45 (Mi izv1527)  

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

A metric theorem on the simultaneous approximation of a zero by the values of integral polynomials

V. I. Bernik


Abstract: In this paper it is proved that the inequality
$$ \prod_{i=1}^k|P(\omega_i)|<H^{-n+k-1-\varepsilon} $$
has only a finite number of solutions in integral polynomials $P(x)$ for almost all $\overline\omega=(\omega_1,…,\omega_k)$. Here $H$ is the coefficient of $P(x)$ largest in absolute value. Sprindzuk's conjecture is thereby proved.
Bibliography: 7 titles.

Full text: PDF file (1465 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1981, 16:1, 21–40

Bibliographic databases:

UDC: 511
MSC: 10F10, 26C10, 30C15
Received: 05.06.1978

Citation: V. I. Bernik, “A metric theorem on the simultaneous approximation of a zero by the values of integral polynomials”, Izv. Akad. Nauk SSSR Ser. Mat., 44:1 (1980), 24–45; Math. USSR-Izv., 16:1 (1981), 21–40

Citation in format AMSBIB
\Bibitem{Ber80}
\by V.~I.~Bernik
\paper A metric theorem on the simultaneous approximation of a~zero by the values of integral polynomials
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1980
\vol 44
\issue 1
\pages 24--45
\mathnet{http://mi.mathnet.ru/izv1527}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=563784}
\zmath{https://zbmath.org/?q=an:0464.10041|0426.10055}
\transl
\jour Math. USSR-Izv.
\yr 1981
\vol 16
\issue 1
\pages 21--40
\crossref{https://doi.org/10.1070/IM1981v016n01ABEH001292}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981LP24600002}


Linking options:
  • http://mi.mathnet.ru/eng/izv1527
  • http://mi.mathnet.ru/eng/izv/v44/i1/p24

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. V. Lebed, V. I. Bernik, “Algebraic points on the plain”, J. Math. Sci., 146:2 (2007), 5680–5685  mathnet  crossref  mathscinet  zmath  elib
    2. N. V. Budarina, D. Dikkinson, V. I. Bernik, “Sovmestnye priblizheniya deistvitelnykh i kompleksnykh chisel algebraicheskimi chislami spetsialnogo vida”, Tr. In-ta matem., 15:1 (2007), 3–9  mathnet
    3. Natalia Budarina, Detta Dickinson, “Simultaneous Diophantine approximation of integral polynomials in the different metrics”, Chebyshevskii sb., 9:1 (2008), 169–184  mathnet  mathscinet
    4. Natalia Budarina, “Simultaneous diophantine approximation in the real and p-adic fields with nonmonotonic error function*”, Lith Math J, 2011  crossref
    5. V. I. Bernik, V. A. Shlyk, “O predstavlenii naturalnykh chisel summoi algebraicheskikh chisel”, Tr. In-ta matem., 19:1 (2011), 3–11  mathnet
    6. I. V. Bulgakov, “Metricheskaya teoriya transtsendentnykh kompleksnykh chisel v oblastyakh maloi mery”, Tr. In-ta matem., 19:1 (2011), 12–21  mathnet
    7. N. V. Budarina, “Metricheskaya teoriya sovmestnykh diofantovykh priblizhenii v $\mathbb{R}^{k}\times\mathbb{C}^{l}\times \mathbb{Q}^m_{p}$”, Chebyshevskii sb., 12:1 (2011), 17–50  mathnet  mathscinet
    8. N. V. Budarina, “Regulyarnye i povsemestnye sistemy dlya sovmestnykh diofantovykh priblizhenii”, Chebyshevskii sb., 12:4 (2011), 43–74  mathnet  mathscinet
    9. E. I. Kovalevskaya, O. V. Rykova, “Razvitie metoda suschestvennykh i nesuschestvennykh oblastei dlya podscheta vektorov s deistvitelnymi algebraicheskimi koordinatami vblizi gladkikh poverkhnostei”, Chebyshevskii sb., 14:4 (2013), 119–126  mathnet
    10. N. V. Shamukova, N. I. Kalosha, “O metricheskikh otsenkakh approksimatsionnykh svoistv znachenii unitarnykh mnogochlenov”, Tr. In-ta matem., 21:1 (2013), 109–122  mathnet
    11. V. I. Bernik, D. V. Vasilev, A. S. Kudin, “O chisle tselochislennykh mnogochlenov zadannoi stepeni i ogranichennoi vysoty s maloi proizvodnoi v korne mnogochlena”, Tr. In-ta matem., 22:2 (2014), 3–8  mathnet
    12. N. V. Budarina, V. I. Bernik, Kh. O'Donnell, “Svyaz faktorizatsii rezultantov i chastoty, s kotoroi oni vstrechayutsya”, Tr. In-ta matem., 22:2 (2014), 9–17  mathnet
    13. N. V. Budarina, V. I. Bernik, F. Gettse, “Effektivnye otsenki mery mnozhestv deistvitelnykh chisel, v kotorykh tselochislennye mnogochleny prinimayut malye znacheniya”, Dalnevost. matem. zhurn., 15:1 (2015), 21–37  mathnet  elib
    14. J. Math. Sci. (N. Y.), 224:2 (2017), 176–198  mathnet  crossref  mathscinet
    15. N. V. Budarina, H. O'Donnell, “Problem of Nesterenko and method of Bernik”, Chebyshevskii sb., 17:4 (2016), 180–184  mathnet  crossref  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:250
    Full text:91
    References:21
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019