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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

CIRM Jean-Morlet Chair, Fall 2016

  • Book
  • © 2018

Overview

Editors:
  1. Sébastien Ferenczi

    1. CNRS UMR 7373, Institut de Mathématiques de Marseille, Marseille, France

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  2. Joanna Kułaga-Przymus

    1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

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    You can also search for this editor in PubMed   Google Scholar

  3. Mariusz Lemańczyk

    1. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

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  • Features a unique, exhaustive list of results and methods concerning the Sarnak and Chowla conjectures
  • Includes a course in analytic number theory accessible to undergraduate students
  • Offers a clear presentation of the interaction of modern dynamics with number theory and combinatorics

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2213)

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Part I

    1. Front Matter

      Pages 1-2
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    2. Prime Numbers

      • Joël Rivat
      Pages 3-10

    3. Arithmetic Functions

      • Joël Rivat
      Pages 11-16

    4. Dirichlet Series

      • Joël Rivat
      Pages 17-23

    5. Euler’s Gamma Function

      • Joël Rivat
      Pages 25-26

    6. Riemann’s Zeta Function

      • Joël Rivat
      Pages 27-52

    7. The Large Sieve

      • Joël Rivat
      Pages 53-78

    8. The Theorem of Vinogradov

      • Joël Rivat
      Pages 79-97

    9. The van der Corput Method

      • Joël Rivat
      Pages 99-113

  3. Interactions Between Arithmetic and Dynamics

    1. Front Matter

      Pages 115-115
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    2. A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems

      • M. Baake
      Pages 117-135

    3. Kloosterman Sums, Disjointness, and Equidistribution

      • M. Einsiedler, M. Luethi
      Pages 137-161

    4. Sarnak’s Conjecture: What’s New

      • Sébastien Ferenczi, Joanna Kułaga-Przymus, Mariusz Lemańczyk
      Pages 163-235

    5. Sarnak’s Conjecture Implies the Chowla Conjecture Along a Subsequence

      • Alexander Gomilko, Dominik Kwietniak, Mariusz Lemańczyk
      Pages 237-247

    6. On the Logarithmic Probability That a Random Integral Ideal Is \( \pmb{\mathcal A}\)-Free

      • Christian Huck
      Pages 249-258

    7. The Lagrange and Markov Spectra from the Dynamical Point of View

      • Carlos Matheus
      Pages 259-291

    8. On the Missing Log Factor

      • Olivier Ramaré
      Pages 293-315

    9. Chowla’s Conjecture: From the Liouville Function to the Moebius Function

      • Olivier Ramaré
      Pages 317-323

  4. Selected Topics in Dynamics

    1. Front Matter

      Pages 325-325
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Keywords

About this book

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 Möbius 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.

Editors and Affiliations

  • CNRS UMR 7373, Institut de Mathématiques de Marseille, Marseille, France

    Sébastien Ferenczi

  • Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

    Joanna Kułaga-Przymus, Mariusz Lemańczyk

Bibliographic Information

  • Book Title: Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

  • Book Subtitle: CIRM Jean-Morlet Chair, Fall 2016

  • Editors: Sébastien Ferenczi, Joanna Kułaga-Przymus, Mariusz Lemańczyk

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-319-74908-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Softcover ISBN: 978-3-319-74907-5Published: 16 June 2018

  • eBook ISBN: 978-3-319-74908-2Published: 15 June 2018

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: IV, 434

  • Number of Illustrations: 223 b/w illustrations, 8 illustrations in colour

  • Topics: Dynamical Systems and Ergodic Theory, Number Theory, Combinatorics, Geometry

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