Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E45

Retrieve articles in all journals with MSC: 22E45


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-73-99952-2
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