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Gaining Units from Units

Published online by Cambridge University Press:  20 November 2018

Leon Bernstein
Leon Bernstein*
Affiliation:
Illinois Institute of Technology, Chicago, Illinois
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Abstract

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Dirichlet was the first to give an ingenious proof of the exact (finite) number of elements in the basis of the multiplicative group of units in any algebraic number field of arbitrary degree n. These elements are called fundamental units. If the field is real and its generating number is a real root of a polynomial over Q of degree n﹜ having r1 real and r2 pairs of conjugate complex roots, so that r1 + 2r2 = n, then Dirichlet's famous result states that the exact number of fundamental units in Q(w) equals r1 + r2 — 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 1 , 01 February 1977 , pp. 93 - 106
Copyright
Copyright © Canadian Mathematical Society 1977

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