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. RAN. Ser. Mat., 2012, Volume 76, Issue 3, Pages 111–138 (Mi izv6035)  

This article is cited in 6 scientific papers (total in 6 papers)

The average number of relative minima of three-dimensional integer lattices of a given determinant

A. A. Illarionov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: We obtain an asymptotic formula for the average number of relative minima of the three-dimensional complete integer lattices of a given determinant. This generalizes Heilbronn's classical result on the average length of a finite continued fraction with a fixed denominator.

Keywords: relative minimum, multidimensional continued fraction, average length of continued fractions.

DOI: https://doi.org/10.4213/im6035

Full text: PDF file (625 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2012, 76:3, 535–562

Bibliographic databases:

UDC: 511.36+511.9
MSC: Primary 11H06; Secondary 11H56, 11H60
Received: 05.11.2010

Citation: A. A. Illarionov, “The average number of relative minima of three-dimensional integer lattices of a given determinant”, Izv. RAN. Ser. Mat., 76:3 (2012), 111–138; Izv. Math., 76:3 (2012), 535–562

Citation in format AMSBIB
\Bibitem{Ill12}
\by A.~A.~Illarionov
\paper The average number of relative minima of three-dimensional integer lattices of a~given determinant
\jour Izv. RAN. Ser. Mat.
\yr 2012
\vol 76
\issue 3
\pages 111--138
\mathnet{http://mi.mathnet.ru/izv6035}
\crossref{https://doi.org/10.4213/im6035}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978110}
\zmath{https://zbmath.org/?q=an:1264.11055}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2012IzMat..76..535I}
\elib{http://elibrary.ru/item.asp?id=20358846}
\transl
\jour Izv. Math.
\yr 2012
\vol 76
\issue 3
\pages 535--562
\crossref{https://doi.org/10.1070/IM2012v076n03ABEH002594}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000305690000005}
\elib{http://elibrary.ru/item.asp?id=17992429}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862682988}


Linking options:
  • http://mi.mathnet.ru/eng/izv6035
  • https://doi.org/10.4213/im6035
  • http://mi.mathnet.ru/eng/izv/v76/i3/p111

    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. A. A. Illarionov, “On the statistical properties of Klein polyhedra in three-dimensional lattices”, Sb. Math., 204:6 (2013), 801–823  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. A. Illarionov, “A multidimensional generalization of Heilbronn's theorem on the average length of a finite continued fraction”, Sb. Math., 205:3 (2014), 419–431  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Russian Math. Surveys, 70:3 (2015), 483–556  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. A. V. Ustinov, “The distribution of solutions of a determinantal equation”, Sb. Math., 206:7 (2015), 988–1019  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. O. Karpenkov, A. Ustinov, “Geometry and combinatoric of Minkowski–Voronoi 3-dimensional continued fractions”, J. Number Theory, 176 (2017), 375–419  crossref  mathscinet  zmath  isi  scopus
    6. A. A. Illarionov, “Distribution of facets of higher-dimensional Klein polyhedra”, Sb. Math., 209:1 (2018), 56–70  mathnet  crossref  crossref  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:367
    Full text:49
    References:39
    First page:11

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