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Algebraic Numbers with Integral Power Traces

✍ Scribed by B. Desmit

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
184 KB
Volume
45
Category
Article
ISSN
0022-314X

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✦ Synopsis

A generalization of the following theorem will be proved. If (\alpha) is an algebraic number of degree (n) over (\mathbb{Q}) and the trace of (\alpha^{i}) lies in (\mathbb{Z}) for all positive (i) up to (n+n \log _{2} n), then (\alpha) is an algebraic integer. 1993 Academic Press. Inc.

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In this paper a trace functional is defined for certain algebras of Fourier integral operators (including, for instance, the algebra of Toeplitz operators on the boundary of a strictly pseudoconvex domain) and it is shown that vanishing of this trace characterizes commutators in each of these algebr