Spherical averages of Siegel transforms for higher rank diagonal actions and applications

Abstract

We investigate the geometry of approximates in multiplicative Diophantine approximation. Our main tool is a new multiparameter averaging result for Siegel transforms on the space of unimodular lattices in ${\mathbb{R}}^n$ which is of independent interest.

arXiv commentNew title. Added comments concerning number fields (see Section 5)

Cited by in corpus (2)

• Equidistribution on homogeneous spaces and the distribution of approximates in Diophantine approximation
• Spiraling of approximations and spherical averages of Siegel transforms