Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics CIRM Jean-Morlet Chair, Fall 2016 /

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Ferenczi, Sébastien (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Kułaga-Przymus, Joanna (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt), Lemańczyk, Mariusz (Επιμελητής έκδοσης, http://id.loc.gov/vocabulary/relators/edt)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Έκδοση: 1st ed. 2018.
• Σειρά: Lecture Notes in Mathematics, 2213
• Θέματα: Dynamics.; Ergodic theory.; Number theory.; Combinatorics.; Geometry.; Dynamical Systems and Ergodic Theory.; Number Theory.

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'...

Πίνακας περιεχομένων:

• 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.