LEADER 04436nam 22006735 450 001 9910300124903321 005 20200702202015.0 010 $a3-319-74908-0 024 7 $a10.1007/978-3-319-74908-2 035 $a(CKB)3810000000358722 035 $a(DE-He213)978-3-319-74908-2 035 $a(MiAaPQ)EBC6302285 035 $a(PPN)229494072 035 $a(EXLCZ)993810000000358722 100 $a20180615d2018 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aErgodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics $eCIRM Jean-Morlet Chair, Fall 2016 /$fedited by Sébastien Ferenczi, Joanna Ku?aga-Przymus, Mariusz Lema?czyk 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (IV, 434 p. 231 illus., 8 illus. in color.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2213 311 $a3-319-74907-2 320 $aIncludes bibliographical references. 327 $aPart 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. 330 $aThis book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2213 606 $aDynamics 606 $aErgodic theory 606 $aNumber theory 606 $aCombinatorial analysis 606 $aGeometry 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010 606 $aGeometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21006 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aNumber theory. 615 0$aCombinatorial analysis. 615 0$aGeometry. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aNumber Theory. 615 24$aCombinatorics. 615 24$aGeometry. 676 $a515.42 702 $aFerenczi$b Sébastien$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aKu?aga-Przymus$b Joanna$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aLema?czyk$b Mariusz$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300124903321 996 $aErgodic theory and dynamical systems in their interactions with arithmetics and combinatorics$91524084 997 $aUNINA