p-adic regulator

Let K, n, r1, r2, {εn,,εr-1}, and ||||i be as in the entry regulatorMathworldPlanetmath, but with K taken to be a CM field.

Define the p-adic logarithm logp:p×p by


Let AK,p be the (r-1)×(r-1) matrix with general entry given by ai,j=logp||εj||i. The absolute valueMathworldPlanetmathPlanetmathPlanetmath of the determinantMathworldPlanetmath of this matrix is again independent of your choice of basis for the units and of the ordering of the embeddingsPlanetmathPlanetmath. This value is called the p-adic regulator of K, and is denoted by Rp,K, or Rp(K).


Title p-adic regulator
Canonical name PadicRegulator
Date of creation 2013-03-22 14:14:13
Last modified on 2013-03-22 14:14:13
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Definition
Classification msc 11R27
Related topic PAdicExponentialAndPAdicLogarithm
Defines p-adic logarithm