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

De La Harpe, Pierre

Pache, Claude

Venkov, Boris B.

English

arXiv

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

Construction of spherical cubature formulas using lattices

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