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Multi-dimensional metric approximation by primitive points

Presented by: 
S G Dani Indian Institute of Technology
Date: 
Friday 4th July 2014 - 13:30 to 14:20
Venue: 
INI Seminar Room 1
Abstract: 
We consider Diophantine inequalities of the form $| \Theta {\bf q} + {\bf p} - {\bf y} |\leq \psi(| {\bf q} |)$, with $\Theta$ is a $n\times m$ matrix with real entries, ${\bf y} \in \mathbb R^n$, $m,n\in {\bf N}$, and $\psi$ is a function on ${\bf N}$ with positive real values, and seek integral solutions ${\bf v} =({\bf q}, {\bf p})^t$ for which the restriction of ${\bf v}$ 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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons