Alessandro Fazzari

activity

20242026

collaborators

5 papers

math.NT2026

Average analytic rank for the $L$ -functions of the elliptic curves $y^{2} = x^{3} - d x$

Chantal David, Lucile Devin, Alessandro Fazzari +1

We study the average analytic rank in the family of $L$ -functions $L (s, E_{d})$ associated with the elliptic curves $E_{d} : y^{2} = x^{3} - d x$ , as $d$ varies over fourth-power-free odd integ…

math.NT2025

Selberg's Central Limit Theorem weighted by Linear Statistics of Zeta Zeros

Alessandro Fazzari, Maxim Gerspach, Paolo Minelli

We consider the value distribution of the logarithm of the Riemann zeta function on the critical line, weighted by the local statistics of zeta zeros. We show that, with appropriat…

math.NT2025

On products of sets of natural density one

Sandro Bettin, Matteo Bordignon, Alessandro Fazzari

In a previous work, Bettin, Koukoulopoulos, and Sanna prove that if two sets of natural numbers $A$ and $B$ have natural density $1$ , then their product set $A \cdot B := \{ab : a…

math.NT2024

The third moment of the logarithm of zeta and a twisted pair correlation conjecture

Alessandro Fazzari, Maxim Gerspach

We prove precise conditional estimates for the third moment of the logarithm of the Riemann zeta function, refining what is implied by the Selberg central limit theorem, both for t…