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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The asymptotic expansion of the zeta-function of a compact semisimple Lie group


Author: Robert S. Cahn
Journal: Proc. Amer. Math. Soc. 54 (1976), 459-462
MathSciNet review: 0397802
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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

$\displaystyle Z(t) = \frac{{\operatorname{Vol} G}} {{{{(4\pi t)}^{\dim G/2}}}}\exp \vert\delta {\vert^2}t + {\text{exponentially small error as }}t \downarrow 0.$


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0397802-3
Keywords: Compact semisimple Lie group, zeta-function, theta function
Article copyright: © Copyright 1976 American Mathematical Society