3 citations · 5 across the 8 of their papers we have counts for
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Spectral quasi correlations and phase-transitions for the nodal length of Arithmetic Random Waves
Andrea Sartori
Spectral quasi correlations are small sums of lattice points lying on the same circle; we show that, for generic integers representable as the sum of two squares, there are no spec…
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…
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 . By averaging over the…
Least primitive root and simultaneous power-non residues
Andrea Sartori
Let be a prime and let be the least primitive root modulo . We prove that for any and large enough the bound \begin{align} g(p)\ll p^{\frac{1}{4\sqrt{e}}+ε}…