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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Lattice points and Lie groups. II

Author: Robert S. Cahn
Journal: Trans. Amer. Math. Soc. 183 (1973), 131-137
MSC: Primary 22E45
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Abstract: Let C be the Casimir operator on a compact, simple, simply connected Lie group G of dimension n. The number of eigenvalues of C, counted with their multiplicities, of absolute value less than or equal to t is asymptotic to $ k{t^{n/2}},\;k$ a constant. This paper shows the error of this estimate to be $ O({t^{2b + a(a - 1)/(a + 1)}})$; where a = rank of G and $ b = {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}(n - a)$.

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Additional Information

PII: S 0002-9947(73)99952-2
Keywords: Compact simple Lie group, lattice points, elliptic operator, Poisson summation formula
Article copyright: © Copyright 1973 American Mathematical Society

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