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Subcoordinate Representation of p-adic Functions and Generalization of Hensel's Lemma
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
2018 (English)In: Izvestiya. Mathematics, ISSN 1064-5632, E-ISSN 1468-4810, Vol. 82, no 3, p. 632-645Article in journal (Refereed) Published
Abstract [en]

In this paper we describe a new representation of p-adic functions, the so-called subcoordinate representation. The main feature of the subcoordinaterepresentation of a p-adic function is that the values of the function f are given in the canonical form of the representation of p-adic numbers. The function f itself is determined by a tuple of p-valued functions from the set {0, 1,..., p-1} into itself and by the order in which these functions are used to determine the values of f. We also give formulae that enable one to pass from the subcoordinate representation of a 1-Lipschitz function to its van der Put series representation. The effective use of the subcoordinate representation of p-adic functions is illustrated by a study of the feasibility of generalizing Hensel's lemma.

Place, publisher, year, edition, pages
Russian Academy of Sciences, 2018. Vol. 82, no 3, p. 632-645
Keywords [en]
p-adic numbers; Lipschitz functions; coordinate representation; van der Put series
National Category
Other Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-61501DOI: 10.1070/IM8578ISI: 000437922000010OAI: oai:DiVA.org:lnu-61501DiVA, id: diva2:1083386
Available from: 2017-03-21 Created: 2017-03-21 Last updated: 2018-07-27Bibliographically approved

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Yurova, EkaterinaKhrennikov, Andrei

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