Simultane Interpolation und P-adische Approximation durch ganzwertige Polynome

Publikation: Beitrag in Buch/Bericht/KonferenzbandBeitrag in Buch/BerichtForschungBegutachtung

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 $P\in\F$.
Titel in ÜbersetzungSimultane Interpolation und P-adische Approximation durch ganzwertige Polynome
Originalspracheenglisch
TitelRings and Factorizations
Redakteure/-innenAlberto Facchini, Marco Fontana, Alfred Geroldinger, Bruce Olberding
Herausgeber (Verlag)Springer, Cham
PublikationsstatusAngenommen/In Druck - 2020

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Schlagwörter

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

ASJC Scopus subject areas

  • !!Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

Dieses zitieren

Frisch, S. (Angenommen/Im Druck). Simultaneous interpolation and P-adic approximation by integer-valued polynomials. in A. Facchini, M. Fontana, A. Geroldinger, & B. Olberding (Hrsg.), Rings and Factorizations Springer, Cham.