Lattice points and Lie groups. III
Author:
Robert S. Cahn
Journal:
Proc. Amer. Math. Soc. 46 (1974), 247-249
MSC:
Primary 22E45
DOI:
https://doi.org/10.1090/S0002-9939-1974-0360935-X
MathSciNet review:
0360935
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Abstract | References | Similar Articles | Additional Information
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 \[ {(4\pi )^{\dim G/2}}\Gamma (\dim G/2 + 1)(1/|w|)\int _{|\Lambda | \leqslant 1} {{f^{{2_{(\Lambda )d\Lambda }}}}.} \]
- Robert S. Cahn, Lattice points and Lie groups. I, II, Trans. Amer. Math. Soc. 183 (1973), 119–129; ibid. 183 (1973), 131–137. MR 335687, DOI https://doi.org/10.1090/S0002-9947-1973-0335687-3
- William Feller, An introduction to probability theory and its applications. Vol. II, John Wiley & Sons, Inc., New York-London-Sydney, 1966. MR 0210154
- S. Minakshisundaram and Å. Pleijel, Some properties of the eigenfunctions of the Laplace-operator on Riemannian manifolds, Canad. J. Math. 1 (1949), 242–256. MR 31145, DOI https://doi.org/10.4153/cjm-1949-021-5
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Additional Information
Keywords:
Compact semisimple group,
Casimir operator,
Laplacian,
zeta function
Article copyright:
© Copyright 1974
American Mathematical Society
