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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Keywords: Compact semisimple group, Casimir operator, Laplacian, zeta function
Article copyright: © Copyright 1974 American Mathematical Society