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Pré-Publication, Document De Travail Année : 2018

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.
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Dates et versions

hal-01705140 , version 1 (09-02-2018)
hal-01705140 , version 2 (03-08-2018)
hal-01705140 , version 3 (07-12-2018)
hal-01705140 , version 4 (01-04-2019)

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José Ibrahim Villanueva Gutiérrez. On the mu and lambda invariants of the logarithmic class group. 2018. ⟨hal-01705140v1⟩
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