Diophantine inheritance for p-adic measures

Datta, Shreyasi ; Ghosh, Anish (2019) Diophantine inheritance for p-adic measures arXiv.org.

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In this paper we prove complete p-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 p-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.

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Deposited On:11 Oct 2021 11:00
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