Kummer generators and lambda invariants
| dc.creator | Hubbard, David | |
| dc.creator | Washington, Lawrence C. | |
| dc.date | 2008-10-09 | |
| dc.date.accessioned | 2026-07-07T10:08:47Z | |
| dc.date.available | 2026-07-07T10:08:47Z | |
| dc.description | Let $F_0=\mathbf Q(\sqrt{-d})$ be an imaginary quadratic field with $3\nmid d$ and let $K_0=\mathbf Q(\sqrt{3d})$. Let $\varepsilon_0$ be the fundamental unit of $K_0$ and let $λ$ be the Iwasawa $λ$-invariant for the cyclotomic $\mathbf Z_3$-extension of $F_0$. The theory of 3-adic $L$-functions gives conditions for $λ\ge 2$ in terms of $ε_0$ and the class numbers of $F_0$ and $K_0$. We construct units of $K_1$, the first level of the $\mathbf Z_3$-extension of $K_0$, that potentially occur as Kummer generators of unramified extensions of $F_1(ζ_3)$ and which give an algebraic interpretation of the condition that $λ\ge 2$. We also discuss similar results on $λ\ge 2$ that arise from work of Gross-Koblitz. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0810.1691 | |
| dc.identifier | http://arxiv.org/abs/0810.1691 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171117 | |
| dc.subject | Number Theory | |
| dc.subject | 11R23; 11R29; 11R27 | |
| dc.title | Kummer generators and lambda invariants | |
| dc.type | text |