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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorVILLANUEVA GUTIÉRREZ, José Ibrahim
dc.date.accessioned2024-04-04T03:01:30Z
dc.date.available2024-04-04T03:01:30Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192907
dc.description.abstractEnLet $\ell$ 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.
dc.language.isoen
dc.title.enOn the mu and lambda invariants of the logarithmic class group
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.identifier.arxiv1802.04006
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-01705140
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01705140v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=VILLANUEVA%20GUTI%C3%89RREZ,%20Jos%C3%A9%20Ibrahim&rft.genre=preprint


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