On the mu and lambda invariants of the logarithmic class group
Résumé
Let l be a rational prime number. Assuming the Gross-Kuz'min conjecture along a Zl-extension K* of a number field K, we show that there exist integers µ, λ and ν such that the exponent e(n) of the order of the logarithmic class group Cl(n) for the n-th layer K(n) of K* is given by e(n) = µl^{n} + λn + ν, for n big enough. We show some relations between the classical invariants µ and λ, and their logarithmic counterparts µ and λ for some class of Zl-extensions. Additionally, we provide numerical examples for the cyclomotic and the non-cyclotomic case.
Domaines
Théorie des nombres [math.NT]
Origine : Fichiers produits par l'(les) auteur(s)
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