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

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Showing 2026 · math.NTShow all

4 papers · 2 filters

math.NT2026

On the inverse Goldbach problem

Paolo Leonetti

We establish two quantitative results concerning additive decompositions of the set $P$ of primes. First, we prove that, if $A, B \subseteq N$ have at least two eleme…

math.NT2026

A characterization of Sophie Germain primes - II

Paolo Leonetti

Let $n \geq 4$ be an even integer. We show that ${1^{σ (1)}, 2^{σ (2)}, \dots, n^{σ (n)}}$ is a complete residue system modulo $n$ for some permutation $σ$ of ${1, 2, \dots, n}$ if and…

math.NT2026

On a question of Ruzsa about densities of sumsets

Paolo Leonetti

Let $d$ , $d^{*}$ , and $d_{*}$ denote, respectively, the asymptotic density, the upper asymptotic density, and the lower asymptotic density on $\mat…

math.NT2026

On the density of $A + B$ when $B$ has few elements

Paolo Leonetti

Let $d$ be the asymptotic density on the positive integers $N^{+}$ . We provide sufficient conditions on an infinite set $B \subseteq N^{+}$ so that for each $…

On the inverse Goldbach problem

A characterization of Sophie Germain primes - II

On a question of Ruzsa about densities of sumsets

On the density of A+B when B has few elements

On the density of $A + B$ when $B$ has few elements