Metrical Theory for Small Linear Forms and Applications to Interference Alignment
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In this paper, the metric theory of Diophantine approximation associated with mixed type small linear forms is investigated. We prove Khintchine–Groshev type theorems for both the real and complex number systems. The motivation for these metrical results comes from their applications in signal processing. One such application is discussed explicitly.
The authors are listed in alphabetical order. We would like to thank Professor Amir Khandani for many useful discussions and guidance. We thank the anonymous referee and Richard Brent for useful comments which have improved the quality and the presentation of the paper. Mumtaz Hussain would like to thank his late mentor Laureate Professor Jonathan Borwein for many fruitful discussions surrounding topics of this paper in particular and number theory in general during his career at the University of Newcastle (Australia). Jon left a lifelong impression on many of us with his breadth of knowledge, sharpness and innovative ideas on nearly every topic.
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