Construction of spherical cubature formulas using lattices

De La Harpe, Pierre; Pache, Claude; Venkov, Boris

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

Scientific article

English

Construction of spherical cubature formulas using lattices

Contributors

De La Harpe, Pierre; Pache, Claude; Venkov, Boris

Published in

St. Petersburg mathematical journal, vol. 18, no. 1, p. 119-139

Publication date

2007

Abstract

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.

Classification

arxiv : math.CO

UNIGE affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

DE LA HARPE, Pierre, PACHE, Claude, VENKOV, Boris. Construction of spherical cubature formulas using lattices. In: St. Petersburg mathematical journal, 2007, vol. 18, n° 1, p. 119–139. doi: 10.1090/S1061-0022-07-00946-6

Article

Identifiers

PID : unige:9802
DOI : 10.1090/S1061-0022-07-00946-6
arXiv : math/0505510

Journal ISSN

1061-0022

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06/07/2010 13:10:00

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06/07/2010 13:10:00

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14/03/2023 15:55:49

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14/03/2023 15:55:49

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29/10/2024 16:17:15

Construction of spherical cubature formulas using lattices

Contributors

Published in

Publication date

Abstract

Classification

UNIGE affiliation entities

Citation (ISO format)

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Journal ISSN

Technical informations

Creation

First validation

Update

Status update

Last indexation