Leopoldt’s conjecture
Let $K$ be a number field^{}, and let $p$ be a rational prime. Then ${R}_{p}(K)\ne 0$, where ${R}_{p}(K)$ denotes the $p$-adic regulator^{} (http://planetmath.org/PAdicRegulator) of $K$.
Though unproven for number fields in general, it is known to be true for abelian extensions^{} of $\mathbb{Q}$, and for certain non-abelian^{} 2-extensions of imaginary quadratic extensions of $\mathbb{Q}$.
References
- 1 L. C. Washington, Introduction to Cyclotomic Fields^{}, Springer-Verlag, New York.
Title | Leopoldt’s conjecture |
---|---|
Canonical name | LeopoldtsConjecture |
Date of creation | 2013-03-22 14:14:28 |
Last modified on | 2013-03-22 14:14:28 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 6 |
Author | mathcam (2727) |
Entry type | Conjecture |
Classification | msc 11R27 |