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Dynamics and Analytic Number Theory

AUD$57.95 inc GST

Part of London Mathematical Society Lecture Note Series

Victor Beresnevich, Felipe Ramírez, Sanju Velani, Yann Bugeaud, Giovanni Forni, Tim Austin, Manfred Einsiedler, Tom Ward, Alex Kontorovich
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  • Date Published: November 2016
  • availability: Available
  • format: Paperback
  • isbn: 9781107552371

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About the Authors
  • Written by leading experts, this book explores several directions of current research at the interface between dynamics and analytic number theory. Topics include Diophantine approximation, exponential sums, Ramsey theory, ergodic theory and homogeneous dynamics. The origins of this material lie in the 'Dynamics and Analytic Number Theory' Easter School held at Durham University in 2014. Key concepts, cutting-edge results, and modern techniques that play an essential role in contemporary research are presented in a manner accessible to young researchers, including PhD students. This book will also be useful for established mathematicians. The areas discussed include ubiquitous systems and Cantor-type sets in Diophantine approximation, flows on nilmanifolds and their connections with exponential sums, multiple recurrence and Ramsey theory, counting and equidistribution problems in homogeneous dynamics, and applications of thin groups in number theory. Both dynamical and 'classical' approaches towards number theoretical problems are also provided.

    • Discusses a broad range of topics within analytic number theory, dynamics, and related subjects
    • Leading experts in the field present current state-of-the-art material
    • Accessible to young researchers, allowing them insight into cutting-edge research
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    Product details

    • Date Published: November 2016
    • format: Paperback
    • isbn: 9781107552371
    • length: 340 pages
    • dimensions: 228 x 152 x 18 mm
    • weight: 0.5kg
    • contains: 10 b/w illus. 35 exercises
    • availability: Available
  • Table of Contents

    1. Metric Diophantine approximation – aspects of recent work Victor Beresnevich, Felipe Ramírez and Sanju Velani
    2. Exponents of Diophantine approximation Yann Bugeaud
    3. Effective equidistribution of nilflows and bounds on Weyl sums Giovanni Forni
    4. Multiple recurrence and finding patterns in dense sets Tim Austin
    5. Diophantine problems and homogeneous dynamics Manfred Einsiedler and Tom Ward
    6. Applications of thin orbits Alex Kontorovich

  • Editors

    Dzmitry Badziahin, University of Durham
    Dzmitry Badziahin is a Reader in the Department of Mathematical Sciences at Durham University. His research interests lie in Diophantine approximation and related areas of ergodic theory, dynamic systems and combinatorics of words.

    Alexander Gorodnik, University of Bristol
    Alexander Gorodnik is a Professor of Mathematics at the University of Bristol. His research interests are in the theory of dynamical systems and its connections with other branches of mathematics such as number theory, geometry and representation theory.

    Norbert Peyerimhoff, University of Durham
    Norbert Peyerimhoff is a Professor of Mathematics at the University of Durham. His research interests lie at the interface between analysis, dynamical systems, discrete geometry and Riemannian geometry.


    Victor Beresnevich, Felipe Ramírez, Sanju Velani, Yann Bugeaud, Giovanni Forni, Tim Austin, Manfred Einsiedler, Tom Ward, Alex Kontorovich

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