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A note on polynomial cycles. (English) Zbl 1053.11021
Let \(p\) be a prime, and let \(C_p\) be the ring of circulant matrices with rational integral entries and order \(p\). The author establishes a connection between cycles of mappings induced by a polynomial \(f\in{\mathbb Z}[X]\) in \(C_p\), and the cycles induced by \(f\) in the ring of integers of the \(p\)-th cyclotomic field.

MSC:
11C08 Polynomials in number theory
11C20 Matrices, determinants in number theory
11R18 Cyclotomic extensions
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References:
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