Traces of high powers of the Frobenius class in the hyperelliptic ensemble
Hardy-Littlewood varieties and semisimple groups.
A metric result on the pair correlation of fractional parts of sequences
Torsion points on curves and common divisors of and
The Leray measure of nodal sets for random eigenfunctions on the torus
We study nodal sets for typical eigenfunctions of the Laplacian on the standard torus in dimensions. Making use of the multiplicities in the spectrum of the Laplacian, we put a Gaussian measure on the eigenspaces and use it to average over the eigenspace. We consider a sequence of eigenvalues with growing multiplicity . The quantity that we study is the Leray, or microcanonical, measure of the nodal set. We show that the expected value of the Leray measure of an eigenfunction is constant,...
Page 1