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
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by P. de la Harpe, C. Pache and B. Venkov

St. Petersburg Math. J. 18 (2007), 119-139

DOI: https://doi.org/10.1090/S1061-0022-07-00946-6

Published electronically: January 19, 2007

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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 $n=4$, $8$, $12$, $14$, $16$, $20$, $23$, 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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