A family of p-adic isometries, fixed points, and the number three
Number Theory
2007-05-23 v1
Abstract
We study a continuous family of norm-preserving isometries of the p-adic unit disk, given as interpolations of a common arithmetic function, the q-analog of the identity, for principal p-adic units q. We show that the fixed point set is trivial except when p=3 and q is a generator of the principal 3-adic units; in that case the isometry given by each q has a unique nontrivial 3-adic fixed point, varying homeomorphically with q.
Cite
@article{arxiv.math/0603387,
title = {A family of p-adic isometries, fixed points, and the number three},
author = {Eric S. Brussel},
journal= {arXiv preprint arXiv:math/0603387},
year = {2007}
}
Comments
25 pages