The light cone Siegel transform, its moment formulas, and their applications

Abstract: In this talk I will describe an analogue of the Siegel transform where the role of Euclidean space is replaced by a light cone corresponding to an indefinite quadratic form.In this case one can use results on the spectral theory of incomplete Eisenstein series to establish moment formulas analogous to the classical formulas of Siegel, Rogers, and Schmidt.I will then describe several applications of these formulas to counting lattice points on the light cone, as well as for the distribution of rational points on the sphere. All new results are based on joint work with Shucheng Yu.

dynamical systemsnumber theory

Audience: general audience

New England Dynamics and Number Theory Seminar