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



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2012, Volume 92, Issue 1, Pages 68–73 (Mi mz9037)  

Representation of Certain Logarithmic Functions as Polynomials with a Small Number of Nonzero Coefficients

V. S. Rainchik

M. V. Lomonosov Moscow State University

Abstract: We study an element of the ring of algebraic integers having the special form $1-z\lambda$. We obtain a formula for calculating its logarithmic functions. Thus, we verify the conjecture that logarithmic functions of the element $1-z\lambda$ are polynomials in $z$ such that $z$ appears only in powers that are divisors of the number of the logarithmic function.

Keywords: logarithmic function, algebraic integer of the form $1-z\lambda$, ring of algebraic integers, algebraic extension of a field, $p$-adic logarithm

DOI: https://doi.org/10.4213/mzm9037

Full text: PDF file (402 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 92:1, 64–69

Bibliographic databases:

UDC: 511.2
Received: 22.10.2010
Revised: 08.12.2011

Citation: V. S. Rainchik, “Representation of Certain Logarithmic Functions as Polynomials with a Small Number of Nonzero Coefficients”, Mat. Zametki, 92:1 (2012), 68–73; Math. Notes, 92:1 (2012), 64–69

Citation in format AMSBIB
\Bibitem{Rai12}
\by V.~S.~Rainchik
\paper Representation of Certain Logarithmic Functions as Polynomials with a Small Number of Nonzero Coefficients
\jour Mat. Zametki
\yr 2012
\vol 92
\issue 1
\pages 68--73
\mathnet{http://mi.mathnet.ru/mz9037}
\crossref{https://doi.org/10.4213/mzm9037}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3201543}
\zmath{https://zbmath.org/?q=an:06138363}
\elib{http://elibrary.ru/item.asp?id=20731569}
\transl
\jour Math. Notes
\yr 2012
\vol 92
\issue 1
\pages 64--69
\crossref{https://doi.org/10.1134/S0001434612070085}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000308042500008}
\elib{http://elibrary.ru/item.asp?id=20473549}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865742132}


Linking options:
  • http://mi.mathnet.ru/eng/mz9037
  • https://doi.org/10.4213/mzm9037
  • http://mi.mathnet.ru/eng/mz/v92/i1/p68

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:287
    Full text:80
    References:42
    First page:20

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020