English

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 α\alpha-theory for ultrametric fields, such as the pp-adics and their extensions, which gives us a multivariate version of Hensel's lemma.

Keywords

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

R2 v1 2026-06-24T11:54:18.766Z