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On representation of cyclotomic fields \({\mathbb Q} (\zeta _{pq})\). (English) Zbl 1024.11067
The correspondence between circulant matrices of degree \(pq\) with \(p,q\) primes and elements of cyclotomic fields \({\mathbb Q}(\zeta _{pq})\) is found. This correspondence is via the determinant of a circulant matrix and the norm of an element of \({\mathbb Q}(\zeta _{pq})\). This correspondence gives a representation for elements of given subfields of the cyclotomic field \({\mathbb Q}(\zeta _{pq})\) by matrices.

MSC:
11R18 Cyclotomic extensions
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References:
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