Type: Seminar

Distribution: World

Expiry: 10 Sep 2013

CalTitle1: AGR Seminar: Measure theoretic results for small linear forms

Auth: mathas@gdh-25.on.site.uni-stuttgart.net in SMS-auth

**Host venue**

University of Newcastle (CARMA)

**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.

**Seminar convenor**

Liangjin Yao

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If you would like to attend this seminar in our access grid room then please check to see if the grid is already booked at this time and send an email to accessgridroom@maths.usyd.edu.au to let the CSOs know that you would like to attend.