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

2014/07/14 by Jayadev S. Athreya, Athreya, Jayadev S., Anish Ghosh +3
Mathematics · #11K60 #37A17 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT #msc:11K60 #msc:37A17

paper · pdf · doi:10.48550/arxiv.1407.3573

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

arxiv created 2015/01/05 · arxiv updated 2015/01/06

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 Rⁿ which is of independent interest.

Related

• Spiraling of approximations and spherical averages of Siegel transforms
• Effective rational approximation on spheres
• Discrete analogues in harmonic analysis: Spherical averages
• Rogers' mean value theorem for S-arithmetic Siegel transform and applications to the geometry of numbers
• Submanifold-genericity of ℝ^d-actions and uniform multiplicative Diophantine approximation