Measure theoretic results for small linear forms

Host Institution:

University of Newcastle (CARMA)

Title of Seminar:

Measure theoretic results for small linear forms

Speaker's Name:

Dr Mumtaz Hussain

Speaker's Institution:

La Trobe University

Time and Date:

Tuesday 10 September 2013, 3.00pm (AEST)

Seminar Abstract:

I will talk about 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. As a consequence we obtain the complete Hausdorff dimension theory. Staying within the absolute value setup, we prove that the corresponding set of badly approximable vectors is of full dimension.

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