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Metrical Theory for Small Linear Forms and Applications to Interference Alignment

  • Mumtaz HussainEmail author
  • Seyyed Hassan Mahboubi
  • Abolfazl Seyed Motahari
Conference paper
  • 48 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 313)

Abstract

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.

Notes

Acknowledgements

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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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Mumtaz Hussain
    • 1
    Email author
  • Seyyed Hassan Mahboubi
    • 1
  • Abolfazl Seyed Motahari
    • 2
  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityBendigoAustralia
  2. 2.Department of Computer EngineeringSharif University of TechnologyTehranIran

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