6 papers
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…
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…
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 -dimensional…
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…
Second Moment of the Prime Geodesic Theorem for
Dimitrios Chatzakos, Giacomo Cherubini, Niko Laaksonen
The remainder in the Prime Geodesic Theorem for the Picard group is known to be bounded by under the assumption of the Li…
A spectral universality theorem for Maass -functions
Giacomo Cherubini, Alberto Perelli
We show that for a positive proportion of Laplace eigenvalues the associated Hecke-Maass -functions approximate with arbitrary precision any target function $f(…