Description
Improvements to Dirichlet’s Theorem in the multiplicative setup and equidistribution of averages along curves
In this talk, I will discuss uniform approximation by rationals vectors in
the multiplicative set-up. Curiously enough, in this context, Dirichlet’s Theorem is improvable, and, for m × n matrices the correct constant is bounded above by 2−m+1. One can also show that almost all matrices are uniformly approximable by the function x−1(logx)−1+ε for any ε > 0. This emerges from the study of certain measures defined by averaging along particular curves the action of the full diagonal group on the space of (m + n)-dimensional unimodular lattices. The talk is based on a joint work with P. Bandi and D. Kleinbock.
