A. Zaccagnini

activity

20052026

most citedThe number of Goldbach representations of an integer

26 citations · 232 across the 37 of their papers we have counts for

collaborators

41 papers

math.NT2026

The average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integer

Alessandra Migliaccio, Alessandro Zaccagnini

We extend a result by Ikeda and Suriajaya (2025) to the average number of representations of an integer as a sum of an arbitrary number $j \geq 3$ of primes. We show that the corresp…

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.NT2026

The average number of representations of an integer as a sum of two prime powers over multiples of a fixed integer

Alessandra Migliaccio, Alessandro Zaccagnini

We extend a result by Ikeda and Suriajaya (2025) to find the asymptotic behaviour of the average number of representations of an integer $n$ , over multiples of a fixed $q \geq 2$ , as…

math.NT2026

On the average number of representations of an integer as a sum of polynomials computed at prime values

Alessandra Migliaccio, Alessandro Zaccagnini

We study the average number of representations of an integer $n$ as $n = ϕ (n_{1}) + \dots + ϕ (n_{j})$ , for polynomials $ϕ \in Z [n]$ with $\partial ϕ = k \geq 1$ , $\operatorname…

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.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.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★ 9 cited

An extension of the Bourgain-Sarnak-Ziegler theorem with modular applications

Mattia Cafferata, Alberto Perelli, Alessandro Zaccagnini

We prove an extension of the Bourgain-Sarnak-Ziegler theorem and then apply it to bound certain polynomial exponential sums with modular coefficients.

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★ 2 cited

Short intervals asymptotic formulae for binary problems with prime powers, II

Alessandro Languasco, Alessandro Zaccagnini

We improve some results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n = p_{1}^{ℓ_{1}} + p_{2}^{ℓ_{2}}$ and $n…

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★ 5 cited

Short intervals asymptotic formulae for binary problems with prime powers

Alessandro Languasco, Alessandro Zaccagnini

We prove results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n = p_{1}^{ℓ_{1}} + p_{2}^{ℓ_{2}}$ , with $\ell_1…

math.NT2018★ 2 cited

A Cesàro average for an additive problem with prime powers

Alessandro Languasco, Alessandro Zaccagnini

In this paper we extend and improve our results on weighted averages for the number of representations of an integer as a sum of two powers of primes. Let $1 \leq ℓ_{1} \leq ℓ_{2}$ …

math.NT2018

Sums of one prime power and two squares of primes in short intervals

Alessandro Languasco, Alessandro Zaccagnini

Let $k \geq 1$ be an integer. We prove that a suitable asymptotic formula for the average number of representations of integers $n = p_{1}^{k} + p_{2}^{2} + p_{3}^{2}$ , where $p_{1}, p_{2}, p_{3}$ …

math.NT2018★ 3 cited

A Cesàro Average of generalised Hardy-Littlewood numbers

Alessandro Languasco, Alessandro Zaccagnini

We continue our recent work on additive problems with prime summands: we already studied the \emph{average} number of representations of an integer as a sum of two primes, and also…

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★ 6 cited

Sums of four prime cubes in short intervals

Alessandro Languasco, Alessandro Zaccagnini

We prove that a suitable asymptotic formula for the average number of representations of integers $n = p_{1}^{3} + p_{2}^{3} + p_{3}^{3} + p_{4}^{3}$ , where $p_{1}, p_{2}, p_{3}, p_{4}$ are prime num…

math.NT2016★ 2 cited

Cesàro average in short intervals for Goldbach numbers

Alessandro Languasco, Alessandro Zaccagnini

We prove that a suitable explicit formula for the Cesaro-averaged number of representations of an integer as a sum of two primes holds in short intervals.

math.NT2016★ 1 cited

The Selberg integral and a new pair-correlation function for the zeros of the Riemann zeta-function

Alessandro Zaccagnini

The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli on our recent investigations on the Selberg integral and its connections to Montgomery's p…

math.NT2015★ 12 cited

Short intervals asymptotic formulae for binary problems with primes and powers, II: density $1$

Alessandro Languasco, Alessandro Zaccagnini

We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime square and a square, or a prime square. Such resu…

math.NT2015★ 5 cited

Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$

Alessandro Languasco, Alessandro Zaccagnini

We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square. Such results are…

The average number of representations of an integer as a sum of three or more primes, over multiples of a fixed integer

On the discrete convolution of the Liouville and Möbius functions

The average number of representations of an integer as a sum of two prime powers over multiples of a fixed integer

On the average number of representations of an integer as a sum of polynomials computed at prime values

Laplace convolutions of weighted averages of arithmetical functions

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

Cesàro averages for Goldbach representations with summands in arithmetic progressions

Signed harmonic sums of integers with k distinct prime factors

An extension of the Bourgain-Sarnak-Ziegler theorem with modular applications

A note on an average additive problem with prime numbers

Short intervals asymptotic formulae for binary problems with prime powers, II

On an average ternary problem with prime powers

Short intervals asymptotic formulae for binary problems with prime powers

A Cesàro average for an additive problem with prime powers

Sums of one prime power and two squares of primes in short intervals

A Cesàro Average of generalised Hardy-Littlewood numbers

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

Sums of four prime cubes in short intervals

Cesàro average in short intervals for Goldbach numbers

The Selberg integral and a new pair-correlation function for the zeros of the Riemann zeta-function

Short intervals asymptotic formulae for binary problems with primes and powers, II: density 1

Short intervals asymptotic formulae for binary problems with primes and powers, I: density 3/2

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

Short intervals asymptotic formulae for binary problems with primes and powers, II: density $1$

Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$