Giacomo Cherubini

activity

20152025

most citedMean square in the prime geodesic theorem

13 citations · 27 across the 10 of their papers we have counts for

collaborators

Showing math.NTShow all

17 papers · 1 filter

math.NT2025

The hyperbolic circle problem over Heegner points

Dimitrios Chatzakos, Giacomo Cherubini, Stephen Lester +1

For the full modular group, we obtain a logarithmic improvement on Selberg's long-standing bound for the error term of the counting function in the hyperbolic circle problem over H…

math.NT2025

Local average in the Hyperbolic sphere problem

Giacomo Cherubini, Christos Katsivelos

We consider a local average in the hyperbolic lattice point counting problem for the Picard group $Γ$ acting on the three-dimensional hyperbolic space. Compared to the pointwise ca…

math.NT2023

There are Salem numbers with trace $- 3$ and every degree at least $34$

Giacomo Cherubini, Pavlo Yatsyna

We prove that there exist Salem numbers with trace $- 3$ and every even degree $\geq 34$ . Our proof combines a theoretical approach, which allows us to treat all sufficiently large…

math.NT2022

Parity of 4-regular and 8-regular partition functions

Giacomo Cherubini, Pietro Mercuri

We give a complete characterization of the parity of $b_{8} (n)$ , the number of $8$ -regular partitions of $n$ . Namely, we prove that $b_{8} (n)$ is odd or even depending on whether or no…

math.NT2022

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…

math.NT2022

Potential energy of totally positive algebraic integers

Giacomo Cherubini, Pavlo Yatsyna

Given positive real numbers, we prove two inequalities involving their potential energy and their power sums. We also prove an inequality involving the energy and the discriminant…

math.NT2021★ 9 cited

Consecutive real quadratic fields with large class numbers

Giacomo Cherubini, Alessandro Fazzari, Andrew Granville +2

For a given positive integer $k$ , we prove that there are at least $x^{1/2 - o (1)}$ integers $d \leq x$ such that the real quadratic fields $\mathbb Q(\sqrt{d+1}),\dots,\mathbb Q(\sqr…

math.NT2020

Cyclic polytope of the simplest cubic fields

Giacomo Cherubini, Pavlo Yatsyna

In this paper, we study dilation of cyclic polytopes with the vertices defined by a generator of the simplest cubic fields. In particular, for a specific range of values, we give a…

math.NT2020

On the variance of the nodal volume of arithmetic random waves

Giacomo Cherubini, Niko Laaksonen

Rudnick and Wigman (Ann. Henri Poincaré, 2008; arXiv:math-ph/0702081) conjectured that the variance of the volume of the nodal set of arithmetic random waves on the $d$ -dimensional…

math.NT2019

Bykovskii-type theorem for the Picard manifold

Antal Balog, András Biró, Giacomo Cherubini +1

We generalise a result of Bykovskii to the Gaussian integers and prove an asymptotic formula for the prime geodesic theorem in short intervals on the Picard manifold. Previous work…

math.NT2019★ 5 cited

On Kuznetsov-Bykovskii's formula of counting prime geodesics

Giacomo Cherubini, Han Wu, Gergely Zábrádi

We generalize a formula on the counting of prime geodesics, due to Kuznetsov-Bykovskii, used in the work of Soundararajan-Young on the prime geodesic theorem. The method works over…

math.NT2018

Second Moment of the Prime Geodesic Theorem for $PSL (2, Z [i])$

Dimitrios Chatzakos, Giacomo Cherubini, Niko Laaksonen

The remainder $E_{Γ} (X)$ in the Prime Geodesic Theorem for the Picard group $Γ = PSL (2, Z [i])$ is known to be bounded by $O (X^{3/2 + ε})$ under the assumption of the Li…

math.NT2018

A spectral universality theorem for Maass $L$ -functions

Giacomo Cherubini, Alberto Perelli

We show that for a positive proportion of Laplace eigenvalues $λ_{j}$ the associated Hecke-Maass $L$ -functions $L (s, u_{j})$ approximate with arbitrary precision any target function $f(…

math.NT2017

Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space

Olga Balkanova, Dimitrios Chatzakos, Giacomo Cherubini +2

For $Γ$ a cofinite Kleinian group acting on $H^{3}$ , we study the Prime Geodesic Theorem on $M = Γ\ H^{3}$ , which asks about the asymptotic behaviour of length…

math.NT2017★ 13 cited

Mean square in the prime geodesic theorem

Giacomo Cherubini, João Guerreiro

We prove upper bounds for the mean square of the remainder in the prime geodesic theorem, for every cofinite Fuchsian group, which improve on average on the best known pointwise bo…

math.NT2016

Almost periodic functions and hyperbolic counting

Giacomo Cherubini

In this paper we prove the existence of asymptotic moments, and an estimate on the tails of the limiting distribution, for a specific class of almost periodic functions. Then we in…

math.NT2015

On the variance of the error term in the hyperbolic circle problem

Giacomo Cherubini, Morten S. Risager

Let $e (s)$ be the error term of the hyperbolic circle problem, and denote by $e_{α} (s)$ the fractional integral to order $α$ of $e (s)$ . We prove that for any small $α > 0$ the asymptot…

The hyperbolic circle problem over Heegner points

Local average in the Hyperbolic sphere problem

There are Salem numbers with trace −3 and every degree at least 34

Parity of 4-regular and 8-regular partition functions

Hyperbolic angles from Heegner points

Potential energy of totally positive algebraic integers

Consecutive real quadratic fields with large class numbers

Cyclic polytope of the simplest cubic fields

On the variance of the nodal volume of arithmetic random waves

Bykovskii-type theorem for the Picard manifold

On Kuznetsov-Bykovskii's formula of counting prime geodesics

Second Moment of the Prime Geodesic Theorem for PSL(2,Z[i])

A spectral universality theorem for Maass L-functions

Prime Geodesic Theorem in the 3-dimensional Hyperbolic Space

Mean square in the prime geodesic theorem

Almost periodic functions and hyperbolic counting

On the variance of the error term in the hyperbolic circle problem

There are Salem numbers with trace $- 3$ and every degree at least $34$

Second Moment of the Prime Geodesic Theorem for $PSL (2, Z [i])$

A spectral universality theorem for Maass $L$ -functions