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., 2011, Volume 75, Issue 5, Pages 103–138 (Mi izv4697)  

This article is cited in 4 scientific papers (total in 4 papers)

The transition constant for arithmetic hyperbolic reflection groups

V. V. Nikulinab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Department of Mathematical Sciences, University of Liverpool

Abstract: Using the results and methods of our papers [1], [2], we show that the degree of the ground field of an arithmetic hyperbolic reflection group does not exceed $25$ in dimensions $n\ge 6$, and $44$ in dimensions $3$$4$$5$. This significantly improves our estimates obtained in [2]–[4]. We also use recent results in [5] and [6] to reduce the last bound to $35$. We also review and correct the results of [1], § 1.

Keywords: group generated by reflections, arithmetic group, hyperbolic space, number field, field of definition, quadratic form.

DOI: https://doi.org/10.4213/im4697

Full text: PDF file (776 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2011, 75:5, 971–1005

Bibliographic databases:

UDC: 512.817.72+512.817.6+511.6
MSC: 20F55, 22E40, 51F15, 51M10
Received: 04.08.2010

Citation: V. V. Nikulin, “The transition constant for arithmetic hyperbolic reflection groups”, Izv. RAN. Ser. Mat., 75:5 (2011), 103–138; Izv. Math., 75:5 (2011), 971–1005

Citation in format AMSBIB
\Bibitem{Nik11}
\by V.~V.~Nikulin
\paper The transition constant for arithmetic hyperbolic reflection groups
\jour Izv. RAN. Ser. Mat.
\yr 2011
\vol 75
\issue 5
\pages 103--138
\mathnet{http://mi.mathnet.ru/izv4697}
\crossref{https://doi.org/10.4213/im4697}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2884665}
\zmath{https://zbmath.org/?q=an:1245.20047}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2011IzMat..75..971N}
\elib{http://elibrary.ru/item.asp?id=20358812}
\transl
\jour Izv. Math.
\yr 2011
\vol 75
\issue 5
\pages 971--1005
\crossref{https://doi.org/10.1070/IM2011v075n05ABEH002561}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000296665700006}
\elib{http://elibrary.ru/item.asp?id=18161044}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80655129443}


Linking options:
  • http://mi.mathnet.ru/eng/izv4697
  • https://doi.org/10.4213/im4697
  • http://mi.mathnet.ru/eng/izv/v75/i5/p103

    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. M. Belolipetsky, B. Linowitz, “On fields of definition of arithmetic Kleinian reflection groups II”, Int. Math. Res. Not. IMRN, 2014:9 (2014), 2559–2571  crossref  mathscinet  zmath  isi  elib  scopus
    2. Belolipetsky M., “Arithmetic hyperbolic reflection groups”, Bull. Amer. Math. Soc., 53:3 (2016), 437–475  crossref  mathscinet  zmath  isi  elib  scopus
    3. Linowitz B., “Bounds For Arithmetic Hyperbolic Reflection Groups in Dimension 2”, Transform. Groups, 23:3 (2018), 743–753  crossref  mathscinet  isi  scopus
    4. Turkalj I., “Reflective Lorentzian Lattices of Signature (5,1)”, J. Algebra, 513 (2018), 516–544  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:368
    Full text:58
    References:28
    First page:7

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