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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lattice points and Lie groups. III


Author: Robert S. Cahn
Journal: Proc. Amer. Math. Soc. 46 (1974), 247-249
MSC: Primary 22E45
MathSciNet review: 0360935
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Abstract: If a compact, simply connected, semisimple Lie group is considered as a Riemannian manifold with metric arising from the negative of the Killing form it is shown that its volume is

$\displaystyle {(4\pi )^{\dim G/2}}\Gamma (\dim G/2 + 1)(1/\vert w\vert)\int_{\vert\Lambda \vert \leqslant 1} {{f^{{2_{(\Lambda )d\Lambda }}}}.} $


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0360935-X
PII: S 0002-9939(1974)0360935-X
Keywords: Compact semisimple group, Casimir operator, Laplacian, zeta function
Article copyright: © Copyright 1974 American Mathematical Society