On the mu and lambda invariants of the logarithmic class group
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | VILLANUEVA GUTIÉRREZ, José Ibrahim | |
| dc.date.accessioned | 2024-04-04T03:01:30Z | |
| dc.date.available | 2024-04-04T03:01:30Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192907 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.title.en | On the mu and lambda invariants of the logarithmic class group | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1802.04006 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01705140 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01705140v1 | |
| bordeaux.COinS | ctx_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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