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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1998, Volume 63, Issue 6, Pages 935–950 (Mi mz1364)

On $p$-adic functions preserving Haar measure

I. A. Yurov

Moscow Engineering Physics Institute (State University)

Abstract: Let $\{a_n\}_{n=0}^\infty$ be a uniformly distributed sequence of $p$-adic integers. In the present paper we study continuous functions close to differentiable ones (with respect to the $p$-adic metric); for these functions, either the sequence $\{f(a_n)\}_{n=0}^\infty$ is uniformly distributed over the ring of $p$-adic integers or, for all sufficiently large $k$, the sequences $\{f_k(\varphi_k(a_n))\}_{n=0}^\infty$ are uniformly distributed over the residue class ring $\operatorname{mod}p^k$, where $\varphi_k$ is the canonical epimorphism of the ring of $p$-adic integers to the residue class ring $\operatorname{mod}p^k$ and $f_k$ is the function induced by $f$ on the residue class ring $\operatorname{mod}p^k$ (i.e., $f_k(x)=f(\varphi_k(x))(\operatorname{mod}p^k)$). For instance, these functions can be used to construct generators of pseudorandom numbers.

DOI: https://doi.org/10.4213/mzm1364

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English version:
Mathematical Notes, 1998, 63:6, 823–836

Bibliographic databases:

UDC: 511.6
Revised: 29.04.1996

Citation: I. A. Yurov, “On $p$-adic functions preserving Haar measure”, Mat. Zametki, 63:6 (1998), 935–950; Math. Notes, 63:6 (1998), 823–836

Citation in format AMSBIB
\Bibitem{Yur98} \by I.~A.~Yurov \paper On $p$-adic functions preserving Haar measure \jour Mat. Zametki \yr 1998 \vol 63 \issue 6 \pages 935--950 \mathnet{http://mi.mathnet.ru/mz1364} \crossref{https://doi.org/10.4213/mzm1364} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1679226} \zmath{https://zbmath.org/?q=an:0920.11051} \transl \jour Math. Notes \yr 1998 \vol 63 \issue 6 \pages 823--836 \crossref{https://doi.org/10.1007/BF02312777} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000076726600036} 

• http://mi.mathnet.ru/eng/mz1364
• https://doi.org/10.4213/mzm1364
• http://mi.mathnet.ru/eng/mz/v63/i6/p935

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This publication is cited in the following articles:
1. Jeong S., “Measure-Preservation and the Existence of a Root of P-Adic 1-Lipschitz Functions in Mahler'S Expansion”, P-Adic Numbers Ultrametric Anal. Appl., 10:3 (2018), 192–208
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