Ultrametric Smale's $\alpha$-theory
Numerical Analysis
2022-12-27 v2 Numerical Analysis
Algebraic Geometry
Number Theory
Abstract
We present a version of Smale's -theory for ultrametric fields, such as the -adics and their extensions, which gives us a multivariate version of Hensel's lemma.
Cite
@article{arxiv.2206.08392,
title = {Ultrametric Smale's $\alpha$-theory},
author = {Jazz G. Suchen and Josué Tonelli-Cueto},
journal= {arXiv preprint arXiv:2206.08392},
year = {2022}
}
Comments
4 pages. 2nd version: Correction of errata in the exponents of main theorem