Francesco Battistoni

activity

20192024

collaborators

8 papers

math.FA2024

A one parameter family of Volterra-type operators

Francesco Battistoni, Giuseppe Molteni

For every $α \in (0, + \infty)$ and $p, q \in (1, + \infty)$ let $T_{α}$ be the operator $L^{p} [0, 1] \to L^{q} [0, 1]$ defined via the equality $(T_{α} f) (x) := \int_{0}^{x^{α}} f (y) d y$ . We study the…

math.NT2021

On the trace of the integers of a number field

Francesco Battistoni, Toufik Zaïmi

Let $T r$ denote the trace $Z$ -module homomorphism defined on the ring $O_{L}$ of the integers of a number field $L .$ We show that $Tr(\mathcal{O}_{L})\varsubset…

math.NT2021

Ranks of elliptic curves over $Q (T)$ of small degree in $T$

Francesco Battistoni, Sandro Bettin, Christophe Delaunay

We study elliptic surfaces over $Q (T)$ with coefficients of a Weierstrass model being polynomials in $Q [T]$ with degree at most 2. We derive an explicit expressio…

math.NT2021

Arithmetic equivalence for non-geometric extensions of global function fields

Francesco Battistoni, Hassan Oukhaba

In this paper we study couples of finite separable extensions of the function field $F_{q} (T)$ which are arithmetically equivalent, i.e. such that prime ideals of $\mathbb{F…

math.NT2021

An elementary proof for a generalization of a Pohst's inequality

Francesco Battistoni, Giuseppe Molteni

Let $P_{n} (y_{1}, \dots, y_{n}) := \prod_{1 \leq i < j \leq n} (1 - \frac{y _{i}}{y _{j}})$ and $P_{n} := sup_{(y_{1}, \dots, y_{n})} P_{n} (y_{1}, \dots, y_{n})$ where the supremum is taken over the $n…

math.NT2019

Discriminants of number fields and surjectivty of trace homomorphism on rings of integers

Francesco Battistoni

In this note we give a brief survey of the most elementary criteria used to determine the surjectivity of the trace operator on the ring of integers of a number field $K$ . Furtherm…

A one parameter family of Volterra-type operators

On the trace of the integers of a number field

Ranks of elliptic curves over Q(T) of small degree in T

Arithmetic equivalence for non-geometric extensions of global function fields

An elementary proof for a generalization of a Pohst's inequality

Discriminants of number fields and surjectivty of trace homomorphism on rings of integers

Ranks of elliptic curves over $Q (T)$ of small degree in $T$