Construction of spherical cubature formulas using lattices

Details Construction of spherical cubature formulas using lattices Construction of spherical cubature formulas using lattices

2005-05-24

arxiv.org/abs/math/0505510v3

Mathematics

Combinatorics

Scientific paper

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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