Leopoldt’s conjecture

Let K be a number fieldMathworldPlanetmath, and let p be a rational prime. Then Rp(K)0, where Rp(K) denotes the p-adic regulatorMathworldPlanetmath (http://planetmath.org/PAdicRegulator) of K.

Though unproven for number fields in general, it is known to be true for abelian extensionsMathworldPlanetmathPlanetmath of , and for certain non-abelianMathworldPlanetmathPlanetmath 2-extensions of imaginary quadratic extensions of .


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