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 Mosc. Math. J., 2008, Volume 8, Number 4, Pages 789–812 (Mi mmj329)

On Ground Fields of Arithmetic Hyperbolic Reflection Groups. II

V. V. Nikulinab

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

Abstract: This paper continues two our papers that appeared in 2007. Using our methods of 1980, 1981, some explicit finite sets of number fields containing all ground fields of arithmetic hyperbolic reflection groups in dimensions at least 4 are defined, and good explicit bounds of their degrees (over $\mathbb Q$) are obtained. This extends the results of our previous paper where it was done in dimensions at least 6. These results could be important for the further classification of these groups.

Key words and phrases: groups generated by reflections, arithmetic groups, hyperbolic groups.

DOI: https://doi.org/10.17323/1609-4514-2008-8-4-789-812

Full text: http://www.ams.org/.../abst8-4-2008.html
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Citation: V. V. Nikulin, “On Ground Fields of Arithmetic Hyperbolic Reflection Groups. II”, Mosc. Math. J., 8:4 (2008), 789–812

Citation in format AMSBIB
\Bibitem{Nik08} \by V.~V.~Nikulin \paper On Ground Fields of Arithmetic Hyperbolic Reflection Groups.~II \jour Mosc. Math.~J. \yr 2008 \vol 8 \issue 4 \pages 789--812 \mathnet{http://mi.mathnet.ru/mmj329} \crossref{https://doi.org/10.17323/1609-4514-2008-8-4-789-812} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2499355} \zmath{https://zbmath.org/?q=an:05518641} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000261829900008} 

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• http://mi.mathnet.ru/eng/mmj/v8/i4/p789

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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. Nikulin V.V., “On ground fields of arithmetic hyperbolic reflection groups. III”, J. Lond. Math. Soc. (2), 79:3 (2009), 738–756
2. Maclachlan C., “Bounds for discrete hyperbolic arithmetic reflection groups in dimension 2”, Bull. Lond. Math. Soc., 43:1 (2011), 111–123
3. V. V. Nikulin, “The transition constant for arithmetic hyperbolic reflection groups”, Izv. Math., 75:5 (2011), 971–1005