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

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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 Harpe^a, C. Pache^a, B. Venkov^b

^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

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\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

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\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.

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\crossref{https://doi.org/10.1090/S1061-0022-07-00946-6}

Linking options:

https://www.mathnet.ru/eng/aa64

https://www.mathnet.ru/eng/aa/v18/i1/p162

This publication is cited in the following 13 articles:

Masatake Hirao, Hiroshi Nozaki, Koji Tasaka, “Spherical designs and modular forms of the $D_4$ lattice”, Res. number theory, 9:4 (2023)
Hakova L., Hrivnak J., Motlochova L., “on Cubature Rules Associated to Weyl Group Orbit Functions”, Acta Polytech., 56:3 (2016), 202–213
Sawa M., Xu Yu., “On Positive Cubature Rules on the Simplex and Isometric Embeddings”, Math. Comput., 83:287 (2014), 1251–1277
St. Petersburg Math. J., 25:4 (2014), 615–646
Eiichi Bannai, Tsuyoshi Miezaki, Developments in Mathematics, 31, Quadratic and Higher Degree Forms, 2013, 1
E. Bannai, Ts. Miezaki, V. A. Yudin, “An elementary approach to toy models for D. H. Lehmer's conjecture”, Izv. Math., 75:6 (2011), 1093–1106
Bannai E., Bannaia E., Hiraob M., Sawab M., “Cubature formulas in numerical analysis and Euclidean tight designs”, European J. Combin., 31:2 (2010), 423–441
Bondarenko A.V., Viazovska M.S., “Spherical designs via Brouwer fixed point theorem”, SIAM J. Discrete Math., 24:1 (2010), 207–217
Bannai E., Miezaki Ts., “Toy models for D. H. Lehmer's conjecture”, J Math Soc Japan, 62:3 (2010), 687–705
V. A. Yudin, “Invariants and Chebyshev polynomials”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S227–S245
Bannai E., Bannai E., “A survey on spherical designs and algebraic combinatorics on spheres”, European J. Combin., 30:6 (2009), 1392–1425
Bondarenko A. V., Viazovska M. S., “New asymptotic estimates for spherical designs”, J. Approx. Theory, 152:1 (2008), 101–106
Scott A. J., “Optimizing quantum process tomography with unitary 2-designs”, J. Phys. A, 41:5 (2008), 055308, 26 pp.

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	185
References:	72
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