Second moment of the light-cone Siegel transform and applications (Q6049888)

The Siegel transform takes a function on \({\mathbb R}^n\) and makes a function on the space of unimodular lattices. The authors apply the spectral approach to study a type of Siegel transform where the Euclidean space is replaced by the light cone of a quadratic form. They prove first and second moment formulas for this transform. New results on intrinsic Diophantine approximations on ellipsoids and the distribution of values of random linear and quadratic forms on the light cone are given.