Construction of spherical cubature formulas using lattices

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

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

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ISSN 1547-7371(online) ISSN 1061-0022(print)

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
Published electronically: January 19, 2007
MathSciNet review: 2225217
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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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