Diophantine inheritance for p-adic measures
Abstract
In this paper we prove complete -adic analogues of Kleinbock's theorems \cite{Kleinbock-extremal, Kleinbock-exponent} on inheritance of Diophantine exponents for affine subspaces. In particular, we answer in the affirmative (and in a stronger form), a conjecture of Kleinbock and Tomanov \cite{KT}, as well as a question of Kleinbock \cite{Kleinbock-exponent}. Our main innovation is the introduction of a new -adic Diophantine exponent which is better suited to homogeneous dynamics, and which we show to be closely related to the exponent considered by Kleinbock and Tomanov.
Cite
@article{arxiv.1903.09362,
title = {Diophantine inheritance for p-adic measures},
author = {Shreyasi Datta and Anish Ghosh},
journal= {arXiv preprint arXiv:1903.09362},
year = {2019}
}
Comments
We have split version 1 into two parts. The present paper addresses the question of inheritance of Diophantine exponents. The multiplicative case and 0-1 dichotomy will appear in a separate paper