A. Zaccagnini

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20052026

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13 papers · 1 filter

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.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

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.

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

Signed harmonic sums of integers with k distinct prime factors

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

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