Lattice points and Lie groups. III
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- by Robert S. Cahn PDF
- Proc. Amer. Math. Soc. 46 (1974), 247-249 Request permission
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 \[ {(4\pi )^{\dim G/2}}\Gamma (\dim G/2 + 1)(1/|w|)\int _{|\Lambda | \leqslant 1} {{f^{{2_{(\Lambda )d\Lambda }}}}.} \]References
- 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 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 10.4153/cjm-1949-021-5
Additional Information
- © Copyright 1974 American Mathematical Society
- 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