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Algebra i Analiz, 2006, Volume 18, Issue 1, Pages 162–186 (Mi aa64)  

This article is cited in 11 scientific papers (total in 11 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

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.

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English version:
St. Petersburg Mathematical Journal, 2007, 18:1, 119–139

Bibliographic databases:

MSC: Primary 65D32, 05B30; Secondary 11F11, 11H06
Received: 03.06.2005
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
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 1
\pages 119--139

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    This publication is cited in the following articles:
    1. Bondarenko A. V., Viazovska M. S., “New asymptotic estimates for spherical designs”, J. Approx. Theory, 152:1 (2008), 101–106  crossref  mathscinet  zmath  isi  elib  scopus
    2. Scott A. J., “Optimizing quantum process tomography with unitary 2-designs”, J. Phys. A, 41:5 (2008), 055308, 26 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. V. A. Yudin, “Invariants and Chebyshev polynomials”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S227–S245  mathnet  crossref  isi  elib
    4. Bannai E., Bannai E., “A survey on spherical designs and algebraic combinatorics on spheres”, European J. Combin., 30:6 (2009), 1392–1425  crossref  mathscinet  zmath  isi  elib  scopus
    5. 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  crossref  mathscinet  zmath  isi  scopus
    6. Bondarenko A.V., Viazovska M.S., “Spherical designs via Brouwer fixed point theorem”, SIAM J. Discrete Math., 24:1 (2010), 207–217  crossref  mathscinet  zmath  isi  elib  scopus
    7. Bannai E., Miezaki Ts., “Toy models for D. H. Lehmer's conjecture”, J Math Soc Japan, 62:3 (2010), 687–705  crossref  mathscinet  zmath  isi  scopus
    8. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    9. St. Petersburg Math. J., 25:4 (2014), 615–646  mathnet  crossref  mathscinet  zmath  isi  elib
    10. Sawa M., Xu Yu., “On Positive Cubature Rules on the Simplex and Isometric Embeddings”, Math. Comput., 83:287 (2014), 1251–1277  crossref  mathscinet  zmath  isi  scopus
    11. Hakova L., Hrivnak J., Motlochova L., “on Cubature Rules Associated to Weyl Group Orbit Functions”, Acta Polytech., 56:3 (2016), 202–213  crossref  isi  elib  scopus
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