Dynamics and Analytic Number Theory

Dzmitry Badziahin, Alexander Gorodnik, Norbert Peyerimhoff

• Publisher: Cambridge University Press
• Year: 2016
• Print ISBN: 9781107552371
• eBook ISBN: 9781316818251
• Topic: Mathematics
• Subtopic: Number Theory
• Index: Mathematics

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.

Table of contents

• Cover
• Series page
• Title page
• Copyright page
• Contents
• List of contributors
• Preface
• 1 Metric Diophantine Approximation: Aspects of Recent Work
• 2 Exponents of Diophantine Approximation
• 3 Effective Equidistribution of Nilflows and Bounds on Weyl Sums
• 4 Multiple Recurrence and Finding Patterns in Dense Sets
• 5 Diophantine Problems and Homogeneous Dynamics
• 6 Applications of Thin Orbits
• Index