# Seminario - Integer-valued polynomials on DVRs of global fields with prescribed lengths of factorizations

domani 6 Ottobre alle ore 15 in Aula 2 riprendono i seminari di Algebra. I prossimi speaker saranno il Dott. Victor Fadinger (University of Graz) e il Dott. Daniel Windisch (TU Graz). Di seguito trovate titoli e abstract dei seminari.

Titolo:
Integer-valued polynomials on DVRs of global fields
with prescribed lengths of factorizations

Abstract:
Let $V$ be a discrete valuation domain whose quotient field $K$ is a
global field.
We show that for all positive integers $k$ and $1 < n_1 \leq \ldots \leq n_k$
there exists an integer-valued polynomial on $V$, that is, an element of
${\rm Int}(V) = \{ f \in K[X] \mid f(V) \subseteq V \}$,
which has precisely $k$ essentially different factorizations into
irreducible elements of ${\rm Int}(V)$ whose lengths are exactly $n_1,\ldots,n_k$.
This solves an open problem proposed by Cahen, Fontana, Frisch and
Glaz in this case.