P. Leonetti

activity

20122026

most citedOn the notions of upper and lower density

20 citations · 109 across the 55 of their papers we have counts for

collaborators

Showing 2019Show all

8 papers · 1 filter

econ.TH2019

Behavioral Equivalence of Extensive Game Structures

Pierpaolo Battigalli, Paolo Leonetti, Fabio Maccheroni

Two extensive game structures with imperfect information are said to be behaviorally equivalent if they share the same map (up to relabelings) from profiles of structurally reduced…

math.NT2019

On the number of gaps of sequences with Poissonian Pair Correlations

Christoph Aistleitner, Thomas Lachmann, Paolo Leonetti +1

A sequence $(x_{n})$ on the torus is said to have Poissonian pair correlations if $# {1 \leq i \neq = j \leq N : ∣ x_{i} - x_{j} ∣ \leq s / N} = 2 s N (1 + o (1))$ for all reals $s > 0$ , as $N \to \infty$ . It…

math.FA2019

A Tauberian theorem for ideal statistical convergence

Marek Balcerzak, Paolo Leonetti

Given an ideal $I$ on the positive integers, a real sequence $(x_{n})$ is said to be $I$ -statistically convergent to $ℓ$ provided that $$ \textstyle \left\{n \…

math.NT2019★ 4 cited

Directions sets: A generalization of ratio sets

Paolo Leonetti, Carlo Sanna

For every integer $k \geq 2$ and every $A \subseteq N$ , we define the \emph{ $k$ -directions sets} of $A$ as $D^{k} (A) := {a /∥ a ∥ : a \in A^{k}}$ and $D^{…

math.FA2019

The general linear equation on open connected sets

Paolo Leonetti, Jens Schwaiger

Fix non-zero reals $α_{1}, \dots, α_{n}$ with $n \geq 2$ and let $K$ be a non-empty open connected set in a topological vector space such that $\sum_{i \leq n} α_{i} K \subseteq K$ (which holds,…

math.NT2019★ 3 cited

Practical numbers among the binomial coefficients

Paolo Leonetti, Carlo Sanna

A "practical number" is a positive integer $n$ such that every positive integer less than $n$ can be written as a sum of distinct divisors of $n$ . We prove that most of the binomia…