-adic regulator
Let , , , , , and be as in the entry regulator, but with taken to be a CM field.
Define the -adic logarithm by
Let be the matrix with general entry given by . The absolute value of the determinant
of this matrix is again independent of your choice of basis for the units and of the ordering of the embeddings
. This value is called the -adic regulator of , and is denoted by , or .
References
-
1
L. C. Washington, Introduction to Cyclotomic Fields
, Springer-Verlag, New York.
Title | -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 | -adic logarithm |