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Metric Diophantine approximation: the absolute value theory

Mumtaz Hussain
(La Trobe University, Melbourne)
Torsdag, 7 juli, 2011, at 15:15-16:15, in Aud. D3 (1531-215)
In the talk I will explain the metrical theory of Diophantine approximation associated with linear forms that are simultaneously small in terms of absolute value rather than the classical nearest integer norm. In other words, we consider linear forms which are simultaneously close to the origin. A complete Khintchine-Groshev type theorem for monotonic approximating functions is established within the absolute value setup. Furthermore, the Hausdorff measure generalization of the Khintchine-Groshev type theorem is obtained. I'll also give an overview of the corresponding set of badly approximable small linear forms.

Kontaktperson: Simon Kristensen