G. Peruginelli

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20112026

most citedIntegral-valued polynomials over the set of algebraic integers of bounded degree

18 citations · 206 across the 29 of their papers we have counts for

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math.NT2024

Nontriviality of rings of integral-valued polynomials

Giulio Peruginelli, Nicholas J. Werner

Let $S$ be a subset of $Z$ , the ring of all algebraic integers. A polynomial $f \in Q [X]$ is said to be integral-valued on $S$ if $f(s) \in \overline{\ma…

math.NT2023★ 1 cited

Stacked Pseudo-Convergent Sequences and Polynomial Dedekind Domains

Giulio Peruginelli

Let $p \in Z$ be a prime, $Q_{p}$ a fixed algebraic closure of the field of $p$ -adic numbers and $Z_{p}$ the absolute integral closure of th…

math.NT2020

On the Lucas and Lehmer sequences in Dedekind domains

Xiumei Li, Giulio Peruginelli, Min Sha

In this paper, we first obtain the strong divisibility property for the Lucas and Lehmer sequences in Dedekind domains, and then establish analogues of Zsigmondy's theorem and the…

math.NT2015★ 10 cited

Adelic versions of the Weierstrass approximation theorem

Jean-Luc Chabert, Giulio Peruginelli

Let $E = \prod_{p \in P} E_{p}$ be a compact subset of $Z = \prod_{p \in P} Z_{p}$ and denote by $\mathcal C(\underline{E},\widehat{\mat…

math.NT2015★ 8 cited

Galois structure on integral valued polynomials

Bahar Heidaryan, Matteo Longo, Giulio Peruginelli

We characterize finite Galois extensions $K$ of the field of rational numbers in terms of the rings $Int_{Q} (O_{K})$ , recently introduced by Loper and Werner,…

math.NT2013★ 18 cited

Integral-valued polynomials over the set of algebraic integers of bounded degree

Giulio Peruginelli

Let $K$ be a number field of degree $n$ with ring of integers $O_{K}$ . By means of a criterion of Gilmer for polynomially dense subsets of the ring of integers of a number field, we…

math.NT2011

On some notions of good reduction for endomorphisms of the projective line

Jung Kyu Canci, Giulio Peruginelli, Dajano Tossici

Let $Φ$ be an endomorphism of $\SR(\bar{\Q})$, the projective line over the algebraic closure of $\Q$, of degree $\geq 2$ defined over a number field $K$ . Let $v$ be a non-archimede…