The asymptotic expansion of the zeta-function of a compact semisimple Lie group
HTML articles powered by AMS MathViewer
- by Robert S. Cahn PDF
- Proc. Amer. Math. Soc. 54 (1976), 459-462 Request permission
Abstract:
If $G$ is a connected, simply connected, semisimple Lie group with metric given by the negative of the Killing form and zeta-function $Z(t)$, then \[ Z(t) = \frac {{\operatorname {Vol} G}} {{{{(4\pi t)}^{\dim G/2}}}}\exp |\delta {|^2}t + {\text {exponentially small error as }}t \downarrow 0.\]References
- S. Bochner, Theta relations with spherical harmonics, Proc. Nat. Acad. Sci. U.S.A. 37 (1951), 804–808. MR 48633, DOI 10.1073/pnas.37.12.804
- Robert S. Cahn, Lattice points and Lie groups. III, Proc. Amer. Math. Soc. 46 (1974), 247–249. MR 360935, DOI 10.1090/S0002-9939-1974-0360935-X
- Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, No. 32, Princeton University Press, Princeton, N.J., 1971. MR 0304972
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 459-462
- DOI: https://doi.org/10.1090/S0002-9939-1976-0397802-3
- MathSciNet review: 0397802