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Izvestiya: Mathematics, 2011, Volume 75, Issue 5, Pages 971–1005
DOI: https://doi.org/10.1070/IM2011v075n05ABEH002561 (Mi im4697) 		 
This article is cited in 6 scientific papers (total in 6 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
English version PDF (517 kB) Citations (6) Russian version article
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DOI: https://doi.org/10.1070/IM2011v075n05ABEH002561
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 $n\geqslant 6$, 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.
Received: 04.08.2010
Bibliographic databases:
Document Type: Article
UDC: 512.817.72+512.817.6+511.6
MSC: 20F55, 22E40, 51F15, 51M10
Language: English
Original paper language: Russian
Citation: V. V. Nikulin, “The transition constant for arithmetic hyperbolic reflection groups”, Izv. Math., 75:5 (2011), 971–1005
Citation in format AMSBIB
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\paper The transition constant for arithmetic hyperbolic reflection groups
\jour Izv. Math.
\yr 2011
\vol 75
\issue 5
\pages 971--1005
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  • https://www.mathnet.ru/eng/im/v75/i5/p103
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:565
    Russian version PDF:168
    English version PDF:21
    References:56
    First page:7
     
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