Geodesic
Gaining Units from Units
Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 93-106

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Bernstein, Leon. Gaining Units from Units. Canadian journal of mathematics, Tome 29 (1977) no. 1, pp. 93-106. doi: 10.4153/CJM-1977-009-5
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