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English

Construction of spherical cubature formulas using lattices

Published inSt. Petersburg mathematical journal, vol. 18, no. 1, p. 119-139
Publication date2007
Abstract

We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on the sphere of dimension 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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  • arxiv : math.CO
Citation (ISO format)
DE LA HARPE, Pierre, PACHE, Claude, VENKOV, Boris. Construction of spherical cubature formulas using lattices. In: St. Petersburg mathematical journal, 2007, vol. 18, n° 1, p. 119–139. doi: 10.1090/S1061-0022-07-00946-6
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ISSN of the journal1061-0022
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