P. Leonetti

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20172022

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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.NT2019

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.NT2019

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…