ON SPRINDŽUK’S CLASSIFICATION OF $p$ -ADIC NUMBERS
We carry Sprindžuk’s classification of the complex numbers to the field $\mathbb{Q}_{p}$ of $p$ -adic numbers. We establish several estimates for the $p$ -adic distance between $p$ -adic roots of integer polynomials, which we apply to show that almost all $p$ -adic numbers, with respect to the Haar...
Saved in:
Published in | Journal of the Australian Mathematical Society (2001) Vol. 111; no. 2; pp. 221 - 231 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Cambridge, UK
Cambridge University Press
01.10.2021
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | We carry Sprindžuk’s classification of the complex numbers to the field
$\mathbb{Q}_{p}$
of
$p$
-adic numbers. We establish several estimates for the
$p$
-adic distance between
$p$
-adic roots of integer polynomials, which we apply to show that almost all
$p$
-adic numbers, with respect to the Haar measure, are
$p$
-adic
$\tilde{S}$
-numbers of order 1. |
---|---|
ISSN: | 1446-7887 1446-8107 |
DOI: | 10.1017/S1446788719000454 |