Publication details

Racines d'unités cyclotomiques et divisibilité du nombre de classes d'un corps abélien réel

Title in English Roots of cyclotomic units and divisibility of the class number of real abelian fields


Year of publication 2001
Type Article in Periodical
Magazine / Source Acta Arithmetica
MU Faculty or unit

Faculty of Science

Field General mathematics
Keywords cyclotomic units
Description The class number $h_K$ of a real abelian field $K$ is known to be difficult to compute. In the paper, $K$ is a genus field of the type $(p,...,p)$ ($l$ times $p$, $p$ is an odd prime). Our main result states that $h_K$ is divisible by $p^{2^l-l^2+l-2}$.
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