VILLANUEVA GUTIÉRREZ, José Ibrahim

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VILLANUEVA GUTIÉRREZ, José Ibrahim
Institut de Mathématiques de Bordeaux [IMB]

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Let $\ell$ be a rational prime number. Assuming the Gross-Kuz'min conjecture along a $\Z_{ell}$-extension $K_{\infty}$ of a number field $K$, we show that there exist integers $\widetilde{\mu}$, $\widetilde{\lambda}$ and $\widetilde{\nu}$ such that the exponent $\tilde{e}_{n}$ of the order $\ell^{\tilde{e}_{n}}$ of the logarithmic class group $\widetilde{C\ell}_{n}$ for the $n$-th layer $K_{n}$ of $K_{\infty}$ is given by $\tilde{e}_{n}=\widetilde{\mu}\ell^{n}+\widetilde{\lambda} n + \widetilde{\nu}$, for $n$ big enough. We show some relations between the classical invariants $\mu$ and $\lambda$, and their logarithmic counterparts $\widetilde{\mu}$ and $\widetilde{\lambda}$ for some class of $\Zl$-extensions. Additionally, we provide numerical examples for the cyclotomic and the non-cyclotomic case.< Leer menos

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On the mu and lambda invariants of the logarithmic class group

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