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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13 papers · 1 filter

math.CA2026

Tauberian rates and the Baire property of ideals

Paolo Leonetti

We study Tauberian conditions on the successive differences of real sequences which ensure that: (i) ordinary convergence coincides with ideal convergence; or (ii) every ordinary a…

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.CA2026

Subadditive bijections on the positive reals

Paolo Leonetti

We show that there exists a subadditive bijection $f : (0, \infty) \to (0, \infty)$ such that $lim inf_{x \to 0} f (x) = 0$ and $lim sup_{x \to 0} f (x) = 1$ . This answers a question by Matkowski…

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 $…

Tauberian rates and the Baire property of ideals

On the inverse Goldbach problem

Subadditive bijections on the positive reals

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