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

Research output: Chapter in Book/Report/Conference proceedingChapter

## 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 contribution Simultane Interpolation und P-adische Approximation durch ganzwertige Polynome English Rings and Factorizations Alberto Facchini, Marco Fontana, Alfred Geroldinger, Bruce Olberding Springer, Cham Accepted/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