Dynamics and Analytic Number Theory 1st Edition by Dzmitry Badziahin, Alexander Gorodnik, Norbert Peyerimhoff ISBN 1107552370 9781107552371
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Product details:
ISBN 10: 1107552370
ISBN 13: 9781107552371
Author: Dzmitry Badziahin, Alexander Gorodnik, Norbert Peyerimhoff
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.
Dynamics and Analytic Number Theory 1st Table of contents:
1 – Metric Diophantine Approximation: Aspects of Recent Work
by Victor Beresnevich (University of York), Felipe Ramírez (Wesleyan University), Sanju Velani (University of York)
pp 1-95
2 – Exponents of Diophantine Approximation
by Yann Bugeaud (Université de Strasbourg)
pp 96-135
3 – Effective Equidistribution of Nilflows and Bounds on Weyl Sums
by Giovanni Forni (University of Maryland)
pp 136-188
4 – Multiple Recurrence and Finding Patterns in Dense Sets
by Tim Austin (Courant Institute, NYU)
pp 189-257
5 – Diophantine Problems and Homogeneous Dynamics
by Manfred Einsiedler (ETH Zürich), Tom Ward (Durham University)
pp 258-288
6 – Applications of Thin Orbits
by Alex Kontorovich (Rutgers University)
pp 289-317
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Tags: Dzmitry Badziahin, Alexander Gorodnik, Norbert Peyerimhoff, Dynamics, Analytic