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Multi-dimensional metric approximation by primitive points

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If you have a question about this talk, please contact Mustapha Amrani.

Interactions between Dynamics of Group Actions and Number Theory

We consider Diophantine inequalities of the form $| Theta {f q} + {f p} – {f y} |leq psi(| {f q} |)$, with $Theta$ is a $n imes m$ matrix with real entries, ${f y} in mathbb Rn$, $m,nin {f N}$, and $psi$ is a function on ${f N}$ with positive real values, and seek integral solutions ${f v} =({f q}, {f p})t$ for which the restriction of ${f v}$ to the components of a given partition $pi$ are primitive integer points. In this setting, we shall discuss metrical results in the style of the Khintchine-Groshev Theorem. Solutions for analogous doubly metrical inequalities will also be discussed.

This talk is part of the Isaac Newton Institute Seminar Series series.

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