9 citations · 14 across the 12 of their papers we have counts for
13 papers
Average analytic rank for the -functions of the elliptic curves
Chantal David, Lucile Devin, Alessandro Fazzari +1
We study the average analytic rank in the family of -functions associated with the elliptic curves , as varies over fourth-power-free odd integ…
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…
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 and have natural density , then their product set $A \cdot B := \{ab : a…
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…
On the joint second moment of zeta and its logarithmic derivative
Alessandro Fazzari
Assuming the Riemann Hypothesis, Goldston, Gonek and Montgomery \cite{GGM} studied the second moment of the log-derivative of , shifted away from the half line by , an…
A Voronoi summation formula for the shifted triple divisor function
Alessandro Fazzari
In this paper, we prove a Voronoi summation formula for the shifted 3-fold divisor function twisted by additive characters. As the main tool, we provide the functional equation for…
A weighted one-level density of the non-trivial zeros of the Riemann zeta-function
Sandro Bettin, Alessandro Fazzari
We compute the one-level density of the non-trivial zeros of the Riemann zeta-function weighted by for and, for test functions with Fourier support in…
Averages of long Dirichlet polynomials with modular coefficients
Brian Conrey, Alessandro Fazzari
We study the moments of -functions associated with primitive cusp forms, in the weight aspect. In particular, we obtain an asymptotic formula for the twisted moments of a \texti…
Hyperbolic angles from Heegner points
Giacomo Cherubini, Alessandro Fazzari
We study lattice points on hyperbolic circles centred at Heegner points of class number one. Our main result is that, on a density one subset of radii tending to infinity, the angl…
Consecutive real quadratic fields with large class numbers
Giacomo Cherubini, Alessandro Fazzari, Andrew Granville +2
For a given positive integer , we prove that there are at least integers such that the real quadratic fields $\mathbb Q(\sqrt{d+1}),\dots,\mathbb Q(\sqr…
A weighted one-level density of families of -functions
Alessandro Fazzari
This paper is devoted to a weighted version of the one-level density of the non-trivial zeros of -functions, tilted by a power of the -function evaluated at the central point…
Weighted value distributions of the Riemann zeta function on the critical line
Alessandro Fazzari
We prove a central limit theorem for with respect to the measure (), assuming RH and the asymptotic formula for twiste…
A weighted central limit theorem for
Alessandro Fazzari
Under the Riemann Hypothesis, we show that as varies in , the distribution of with respect to the measure is approximately…