Simultaneous interpolation and P-adic approximation by integer-valued polynomials

Research output: Chapter in Book/Report/Conference proceedingChapterResearchpeer-review

Abstract

Let $D$ be a Dedekind domain with finite residue fields
and $\F$ a finite set of maximal ideals of $D$.
Let $r_0$, $\ldots$, $r_n$ be distinct elements of $D$,
pairwise incongruent modulo $P^\kP$ for each $P\in\F$,
and $s_0$, $\ldots$, $s_n$ arbitrary elements of $D$.

We show that there is an interpolating $P^\kP$-congruence
preserving integer-valued polynomial, that is,
$f\in \Int(D)=\{g\in K[x]\mid g(D)\subseteq D\}$
with $f(r_i)=s_i$ for $0\le i \le n$, such that, moreover, the
function $f\colon D\rightarrow D$ is constant modulo $P^\kP$
on each residue class of $P^\kP$ for all $P\in\F$.
Translated title of the contributionSimultane Interpolation und P-adische Approximation durch ganzwertige Polynome
Original languageEnglish
Title of host publicationRings and Factorizations
EditorsAlberto Facchini, Marco Fontana, Alfred Geroldinger, Bruce Olberding
PublisherSpringer, Cham
Publication statusAccepted/In press - 2020

Keywords

  • Interpolation
  • polynomials
  • P-adic approximation
  • P-adic Lipschitz functions
  • polynomial functions
  • polynomial mappings
  • congruence preserving
  • integer-valued polynomials
  • Dedekind domains
  • commutative rings
  • integral domains

ASJC Scopus subject areas

  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

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  • Cite this

    Frisch, S. (Accepted/In press). Simultaneous interpolation and P-adic approximation by integer-valued polynomials. In A. Facchini, M. Fontana, A. Geroldinger, & B. Olberding (Eds.), Rings and Factorizations Springer, Cham.