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GAN

Seminar

Multi-dimensional metric approximation by primitive points

Dani, S G (Indian Institute of Technology)
Friday 04 July 2014, 13:30-14:20

Seminar Room 1, Newton Institute

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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