lnu.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Generalization of Hensel's lemma: Finding the roots of p-adic Lipschitz functions
Linnaeus University, Faculty of Technology, Department of Mathematics. (International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science)ORCID iD: 0000-0003-1919-1495
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2016 (English)In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 158, 217-233 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we consider the problem of finding the roots of p-adic functions. In the case, where the function is defined by a polynomial with integer p-adic coefficients, using Hensel's lifting lemma helps us find the roots of the p-adic function.

We generalize Hensel's lifting lemma for a wider class of p  -adic functions, namely, the functions which satisfy the Lipschitz condition with constant , in particular, the functions of this class may be non-differentiable. The paper also presents an iterative procedure for finding approximate (in p  -adic metric) values of the root of pα-Lipschitz functions, thus generalizing the p-adic analogue of Newton's method for such a class of functions.

Place, publisher, year, edition, pages
2016. Vol. 158, 217-233 p.
Keyword [en]
p-Adics; Hensel's lifting lemma; Lipschitz function; Van der Put series
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-46723DOI: 10.1016/j.jnt.2015.06.004ISI: 000362625500012OAI: oai:DiVA.org:lnu-46723DiVA: diva2:860254
Available from: 2015-10-12 Created: 2015-10-12 Last updated: 2016-05-03Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Yurova Axelsson, EkaterinaKhrennikov, Andrei
By organisation
Department of Mathematics
In the same journal
Journal of Number Theory
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 197 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf