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

CIRM Jean-Morlet Chair, Fall 2016

Häftad, Engelska, 2018

Av Sébastien Ferenczi, Joanna Kułaga-Przymus, Mariusz Lemańczyk, Sebastien Ferenczi, Joanna Kulaga-Przymus, Mariusz Lemanczyk, Joanna Ku¿aga-Przymus, Mariusz Lema¿czyk

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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.

Produktinformation

Utgivningsdatum2018-06-16
Mått155 x 235 x 27 mm
Vikt684 g
FormatHäftad
SpråkEngelska
SerieLecture Notes in Mathematics
Antal sidor434
FörlagSpringer International Publishing AG
ISBN9783319749075

Tillhör följande kategorier

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.