Dynamics and Analytic Number Theory (Paperback)

Dzmitry Badziahin

ISBN 10: 1107552370 / ISBN 13: 9781107552371

Editore: Cambridge University Press, Cambridge, 2016

Paperback. 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. Aimed at both young and established researchers, this book covers several directions of current research lying at the interface between dynamics and analytic number theory. Leading experts present a wide range of topics, including homogeneous dynamics, Diophantine approximation, Ramsey theory, ergodic theory and combinatorics. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Codice articolo 9781107552371

Riassunto:

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.

Informazioni sugli autori: 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.

Dati bibliografici

Titolo: Dynamics and Analytic Number Theory (...
Casa editrice: Cambridge University Press, Cambridge
Data di pubblicazione: 2016
Legatura: Paperback
Condizione: new