
Dynamics and Analytic Number Theory
Cambridge University Press
Published on 10. November 2016
Book
Paperback/Softback
340 pages
978-1-107-55237-1 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises; 7 Halftones, black and white; 3 Line drawings, black and white
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 20 mm
Weight
553 gr
ISBN-13
978-1-107-55237-1 (9781107552371)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Dzmitry Badziahin
Dynamics and Analytic Number Theory
E-Book
11/2016
Cambridge University Press
€57.99
Available for download

Dzmitry Badziahin | Alexander Gorodnik | Norbert Peyerimhoff
Dynamics and Analytic Number Theory
E-Book
10/2016
Cambridge University Press
€69.49
Available for download
Persons
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 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 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.
Editor
University of Durham
University of Bristol
University of Durham
Content
1. Metric Diophantine approximation - aspects of recent work Victor Beresnevich, Felipe Ramirez 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; Index.