Leopoldt’s conjecture

Let $K$ be a number field, and let $p$ be a rational prime. Then $R_{p}(K)\neq 0$ , 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