Geodesic
Subcoordinate representation of $p$-adic functions and generalization of Hensel's lemma
Izvestiya. Mathematics , Tome 82 (2018) no. 3, pp. 632-645

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In this paper we describe a new representation of $p$-adic functions, the so-called subcoordinate representation. The main feature of the subcoordinate representation 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 $\{0,1,\dots,p-1\}$ 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.
Keywords: $p$-adic numbers, Lipschitz functions, coordinate representation, van der Put series. 
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     author = {E. I. Yurova Axelsson and A. Yu. Khrennikov},
     title = {Subcoordinate representation of $p$-adic functions and generalization of {Hensel's} lemma},
     journal = {Izvestiya. Mathematics },
     pages = {632--645},
     publisher = {mathdoc},
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     number = {3},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a9/}
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E. I. Yurova Axelsson; A. Yu. Khrennikov. Subcoordinate representation of $p$-adic functions and generalization of Hensel's lemma. Izvestiya. Mathematics , Tome 82 (2018) no. 3, pp. 632-645. http://geodesic.mathdoc.fr/item/IM2_2018_82_3_a9/