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

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Cover of 'Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics'

Table of Contents

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    Book Overview
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    Chapter 1 Prime Numbers
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    Chapter 2 Arithmetic Functions
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    Chapter 3 Dirichlet Series
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    Chapter 4 Euler’s Gamma Function
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    Chapter 5 Riemann’s Zeta Function
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    Chapter 6 The Large Sieve
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    Chapter 7 The Theorem of Vinogradov
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    Chapter 8 The van der Corput Method
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    Chapter 9 A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems
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    Chapter 10 Kloosterman Sums, Disjointness, and Equidistribution
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    Chapter 11 Sarnak’s Conjecture: What’s New
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    Chapter 12 Sarnak’s Conjecture Implies the Chowla Conjecture Along a Subsequence
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    Chapter 13 On the Logarithmic Probability That a Random Integral Ideal Is A $$ \pmb{\mathcal A}$$ -Free
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    Chapter 14 The Lagrange and Markov Spectra from the Dynamical Point of View
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    Chapter 15 On the Missing Log Factor
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    Chapter 16 Chowla’s Conjecture: From the Liouville Function to the Moebius Function
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    Chapter 17 Weak Mixing for Infinite Measure Invertible Transformations
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    Chapter 18 More on Tame Dynamical Systems
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    Chapter 19 A Piecewise Rotation of the Circle, IPR Maps and Their Connection with Translation Surfaces
Attention for Chapter 1: Prime Numbers
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