Andrea Sartori

activity

20182021

collaborators

5 papers

math.PR2021

On the behavior of nodal lines near the boundary for Laplace eigenfunctions on the square

Oleksiy Klurman, Andrea Sartori

We are interested in the effect of Dirichlet boundary conditions on the nodal length of Laplace eigenfunctions. We study random Gaussian Laplace eigenfunctions on the two dimension…

math.PR2021

Expected nodal volume for non-Gaussian random band-limited functions

Zakhar Kabluchko, Andrea Sartori, Igor Wigman

The asymptotic law for the expected nodal volume of random non-Gaussian monochromatic band-limited functions is determined in vast generality. Our methods combine microlocal analyt…

math.NT2019

Planck-scale number of nodal domains for toral eigenfunctions

Andrea Sartori

We study the number of nodal domains in balls shrinking slightly above the Planck scale for "generic" toral eigenfunctions. We prove that, up to the natural scaling, the nodal doma…

math.NT2018

Mass distribution for toral eigenfunctions via Bourgain's de-randomisation

Andrea Sartori

We study the problem of mass distribution of Laplacian eigenfunctions in shrinking balls for the standard flat torus $T^{2} = R^{2} / Z^{2}$ . By averaging over the…

math.NT2018

Least primitive root and simultaneous power-non residues

Andrea Sartori

Let $p$ be a prime and let $g (p)$ be the least primitive root modulo $p$ . We prove that for any $ε > 0$ and $p$ large enough the bound \begin{align} g(p)\ll p^{\frac{1}{4\sqrt{e}}+ε}…