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Algebra i Analiz, 2006, Volume 18, Issue 1, Pages 162–186 (Mi aa64)  
This article is cited in 13 scientific papers (total in 13 papers)

Research Papers

Construction of spherical cubature formulas using lattices

P. de la Harpea, C. Pachea, B. Venkovb

a Section de Mathématiques, Université de Genève, Genève, Switzerland
b Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia
Full-text PDF (277 kB) Citations (13)
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Abstract: We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidean lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on $\mathbb S^{n-1}$ for $n=4$, 8, 12, 14, 16, 20, 23, and 24, and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming.
Received: 03.06.2005
English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 1, Pages 119–139
DOI: https://doi.org/10.1090/S1061-0022-07-00946-6
Bibliographic databases:
Document Type: Article
MSC: Primary 65D32, 05B30; Secondary 11F11, 11H06
Language: English
Citation: P. de la Harpe, C. Pache, B. Venkov, “Construction of spherical cubature formulas using lattices”, Algebra i Analiz, 18:1 (2006), 162–186; St. Petersburg Math. J., 18:1 (2007), 119–139
Citation in format AMSBIB
\Bibitem{De PacVen06}
\by P.~de la Harpe, C.~Pache, B.~Venkov
\paper Construction of spherical cubature formulas using lattices
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 1
\pages 162--186
\mathnet{http://mi.mathnet.ru/aa64}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2225217}
\zmath{https://zbmath.org/?q=an:1122.65028}
\elib{https://elibrary.ru/item.asp?id=9212603}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 1
\pages 119--139
\crossref{https://doi.org/10.1090/S1061-0022-07-00946-6}
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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    Full-text PDF :171
    References:65
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