Diophantine approximation on affine subspaces

Abstract: We extend the classical theorem of Khintchine on metric diophantine approximation to affine subspaces of $\mathbf{R}^n$. In order to achieve this it is necessary to impose some condition on the diophantine exponent of the matrix defining the affine subspace. Our result actually concerns the more general Hausdorff measure, which is known as the generalized Baker-Schmidt problem. We solve this problem by establishing optimal estimates for the number of rational points lying close to the affine subspace.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

Registration for the conference is free. Register at cant2021.eventbrite.com.

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