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Ergodic theory and dynamical systems...

Ferenczi, Sebastien.

Ergodic theory and dynamical systems in their interactions with arithmetics and combinatoricsCIRM Jean-Morlet Chair, Fall 2016 /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Ergodic theory and dynamical systems in their interactions with arithmetics and combinatoricsedited by Sebastien Ferenczi, Joanna Kulaga-Przymus, Mariusz Lemanczyk.
Reminder of title:	CIRM Jean-Morlet Chair, Fall 2016 /
other author:	Ferenczi, Sebastien.
Published:	Cham :Springer International Publishing :2018.
Description:	iv, 434 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Number theory.
Online resource:	http://dx.doi.org/10.1007/978-3-319-74908-2
ISBN:	9783319749082$q(electronic bk.)

Ergodic theory and dynamical systems in their interactions with arithmetics and combinatoricsCIRM Jean-Morlet Chair, Fall 2016 /
Ergodic theory and dynamical systems in their interactions with arithmetics and combinatoricsCIRM Jean-Morlet Chair, Fall 2016 /[electronic resource] :edited by Sebastien Ferenczi, Joanna Kulaga-Przymus, Mariusz Lemanczyk. - Cham :Springer International Publishing :2018. - iv, 434 p. :ill. (some col.), digital ;24 cm. - Lecture notes in mathematics,22130075-8434 ;. - Lecture notes in mathematics ;2035..

Part I. Bases of Analytic Number Theory -- 1. Prime Numbers -- 2. Arithmetic Functions -- 3. Dirichlet Series -- 4. Euler's Gamma Function -- 5. Riemann's Zeta Function -- 6. The Large Sieve -- 7. The Theorem of Vinogradov -- 8. The van der Corput Method -- Part II. Interactions Between Arithmetics and Dynamics -- 9. A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems -- 10. Kloosterman Sums, Disjointness, and Equidistribution -- 11. Sarnak's Conjecture - what's new -- 12. Sarnak's Conjecture Implies the Chowla Conjecture Along a Subsequence -- 13. On the Logarithmic Probability that a Random Integral Ideal is A-free -- 14. The Lagrange and Markov Spectra from the Dynamical Point of View -- 15. On the missing Log Factor -- 16. Chowla's Conjecture: From the Liouville Function to the Moebius Function -- Part III. Selected Topics in Dynamics -- 17. Weak Mixing for Infinite Measure Invertible Transformations -- 18. More on Tame Dynamical Systems -- 19. A Piecewise Rotation of the Circle, IPR Maps and Their Connection with Translation Surfaces.

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Mobius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

ISBN: 9783319749082$q(electronic bk.)

Standard No.: 10.1007/978-3-319-74908-2doiSubjects--Topical Terms:

189521
Number theory.

LC Class. No.: QA241 / .E746 2018

Dewey Class. No.: 512.7

Ergodic theory and dynamical systems in their interactions with arithmetics and combinatoricsCIRM Jean-Morlet Chair, Fall 2016 /
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505 0 $a Part I. Bases of Analytic Number Theory -- 1. Prime Numbers -- 2. Arithmetic Functions -- 3. Dirichlet Series -- 4. Euler's Gamma Function -- 5. Riemann's Zeta Function -- 6. The Large Sieve -- 7. The Theorem of Vinogradov -- 8. The van der Corput Method -- Part II. Interactions Between Arithmetics and Dynamics -- 9. A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems -- 10. Kloosterman Sums, Disjointness, and Equidistribution -- 11. Sarnak's Conjecture - what's new -- 12. Sarnak's Conjecture Implies the Chowla Conjecture Along a Subsequence -- 13. On the Logarithmic Probability that a Random Integral Ideal is A-free -- 14. The Lagrange and Markov Spectra from the Dynamical Point of View -- 15. On the missing Log Factor -- 16. Chowla's Conjecture: From the Liouville Function to the Moebius Function -- Part III. Selected Topics in Dynamics -- 17. Weak Mixing for Infinite Measure Invertible Transformations -- 18. More on Tame Dynamical Systems -- 19. A Piecewise Rotation of the Circle, IPR Maps and Their Connection with Translation Surfaces.
520 $a This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Mobius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.
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