 CARMA OANT SEMINAR
 Speaker: Dr Mumtaz Hussain, CARMA, The University of Newcastle
 Title: Measure theoretic results for small linear forms
 Location: Room V205, Mathematics Building (Callaghan Campus) The University of Newcastle
 Access Grid Venue: CARMA [ENQUIRIES]
 Time and Date: 3:00 pm, Tue, 10^{th} Sep 2013
 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 KhintchineGroshev type theorem for monotonic approximating functions is established within the absolute value setup. Furthermore, the Hausdorff measure generalization of the KhintchineGroshev 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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