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Diophantine Approximation and applications in Interference Alignment

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JournalAdvances in Mathematics
DateAccepted/In press - 4 Jul 2016
DateE-pub ahead of print - 27 Jul 2016
DatePublished (current) - 22 Oct 2016
Volume302
Number of pages49
Pages (from-to)231-279
Early online date27/07/16
Original languageEnglish

Abstract

This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable advances in this area give substantial credit to the fundamental Khintchine-Groshev Theorem and, in particular, to its far reaching generalisation for submanifolds of a Euclidean space. With a view towards the aforementioned applications, here we introduce and prove quantitative explicit generalisations of the Khintchine-Groshev Theorem for non-degenerate submanifolds of R n. The importance of such quantitative statements is explicitly discussed in Jafar's monograph [12, §4.7.1].

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©2016 The Author(s). Published by Elsevier Inc

    Research areas

  • Khintchine-Groshev Theorem, Metric Diophantine approximation, Non-degenerate manifolds

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