Alessandro Gambini

activity

20172026

most citedOn the average number of representations of an integer as a sum of like prime powers

4 citations · 7 across the 14 of their papers we have counts for

collaborators

15 papers

math.NT2026

On the discrete convolution of the Liouville and Möbius functions

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

In this article we study some properties of the discrete convolution of Liouville function $S (n) := \sum_{m_{1} + m_{2} = n} λ (m_{1}) λ (m_{2})$ , which is a Goldbach-t…

math.NT2025

On Eswarathasan--Levine and Boyd's conjectures for harmonic numbers

Leonardo Carofiglio, Giacomo Cherubini, Alessandro Gambini

We provide numerical evidence towards three conjectures on harmonic numbers by Eswarathasan--Levine and Boyd. Let $J_{p}$ denote the set of integers $n \geq 1$ such that the harmonic…

math.NT2024

Diophantine approximation with a quaternary problem

Alessandro Gambini

Let $1 < k < 7/6$ , $λ_{1}, λ_{2}, λ_{3}$ and $λ_{4}$ be non-zero real numbers, not all of the same sign such that $λ_{1} / λ_{2}$ is irrational and let $ω$ be a real number. We prove that the inequali…

math.NT2024

Laplace convolutions of weighted averages of arithmetical functions

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

Let $G (g; x) := \sum_{n \leq x} g (n)$ be the summatory function of an arithmetical function $g (n)$ . In this paper, we prove that we can write weighted averages of an arbitrary fixed num…

math.NT2023★ 1 cited

$p$ -adic valuation of harmonic sums and their connections with Wolstenholme primes

Leonardo Carofiglio, Luigi De Filpo, Alessandro Gambini

We explore a conjecture posed by Eswarathasan and Levine on the distribution of $p$ -adic valuations of harmonic numbers $H (n) = 1 + 1/2 + \dots + 1/ n$ that states that the set $J_{p}$ of th…

math.NT2020★ 1 cited

A Cesàro average for an additive problem with an arbitrary number of prime powers and squares

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

In this paper we extend and improve all the previous results known in literature about weighted average, with Cesàro weight, of representations of an integer as sum of a positive a…

math.NT2020

On the distribution of the digits of quotients of integers and primes

Alessandro Gambini, Remis Tonon, Alessandro Zaccagnini

We investigate the distribution of the digits of quotients of randomly chosen positive integers taken from the interval $[1, T]$ , improving the previously known error term for the c…

math.CA2020

Identities for Catalan's constant arising from integrals depending on a parameter

Federica Ferretti, Alessandro Gambini, Daniele Ritelli

In this paper we provide some relationships between Catalan's constant and the $_{3} F_{2}$ and $_{4} F_{3}$ hypergeometric functions, deriving them from some parametric integral…

math.NT2019

Cesàro averages for Goldbach representations with summands in arithmetic progressions

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

We consider weighted averages of the number of representations of an even integer as a sum of two prime numbers, where each summand lies in a given arithmetic progression modulo a…

math.NT2019

Signed harmonic sums of integers with $k$ distinct prime factors

Alessandro Gambini, Remis Tonon, Alessandro Zaccagnini

We give some theoretical and computational results on "random" harmonic sums with prime numbers, and more generally, for integers with a fixed number of prime factors.

math.NT2019

A note on an average additive problem with prime numbers

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interva…

math.NT2018

On an average ternary problem with prime powers

Marco Cantarini, Alessandro Gambini, Alessandro Languasco +1

We continue our recent work on averages for ternary additive problems with powers of prime numbers.

math.NT2018★ 4 cited

On the average number of representations of an integer as a sum of like prime powers

Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini

We investigate the average number of representations of a positive integer as the sum of $k + 1$ perfect $k$ -th powers of primes. We extend recent results of Languasco and the last…

math.NT2017

A Diophantine approximation problem with two primes and one $k$ -th power of a prime

Alessandro Gambini, Alessandro Languasco, Alessandro Zaccagnini

We refine a result of the last two Authors of [8] on a Diophantine approximation problem with two primes and a $k$ -th power of a prime which was only proved to hold for $1 < k < 4/3$ .…

math.NT2017★ 1 cited

Diophantine approximation with one prime, two squares of primes and one $k$ -th power of a prime

Alessandro Gambini

Let $1 < k < 14/5$ , $λ_{1}, λ_{2}, λ_{3}$ and $λ_{4}$ be non-zero real numbers, not all of the same sign such that $λ_{1} / λ_{2}$ is irrational and let $ω$ be a real number. We prove that the inequal…

On the discrete convolution of the Liouville and Möbius functions

On Eswarathasan--Levine and Boyd's conjectures for harmonic numbers

Diophantine approximation with a quaternary problem

Laplace convolutions of weighted averages of arithmetical functions

p-adic valuation of harmonic sums and their connections with Wolstenholme primes

A Cesàro average for an additive problem with an arbitrary number of prime powers and squares

On the distribution of the digits of quotients of integers and primes

Identities for Catalan's constant arising from integrals depending on a parameter

Cesàro averages for Goldbach representations with summands in arithmetic progressions

Signed harmonic sums of integers with k distinct prime factors

A note on an average additive problem with prime numbers

On an average ternary problem with prime powers

On the average number of representations of an integer as a sum of like prime powers

A Diophantine approximation problem with two primes and one k-th power of a prime

Diophantine approximation with one prime, two squares of primes and one k-th power of a prime

$p$ -adic valuation of harmonic sums and their connections with Wolstenholme primes

Signed harmonic sums of integers with $k$ distinct prime factors

A Diophantine approximation problem with two primes and one $k$ -th power of a prime

Diophantine approximation with one prime, two squares of primes and one $k$ -th power of a prime