Construction of spherical cubature formulas using lattices

de la Harpe, P.; Pache, C.; Venkov, B.

doi:10.1090/S1061-0022-07-00946-6

Construction of spherical cubature formulas using lattices

Authors: P. de la Harpe, C. Pache and B. Venkov
Original publication: Algebra i Analiz, tom 18 (2006), nomer 1.
Journal: St. Petersburg Math. J. 18 (2007), 119-139
MSC (2000): Primary 65D32, 05B30; Secondary 11F11, 11H06
DOI: https://doi.org/10.1090/S1061-0022-07-00946-6
Published electronically: January 19, 2007
MathSciNet review: 2225217
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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 , , , , , , , and , and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming.

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