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Dynamics and analytic number theory.
Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
[Place of publication not identified] :
Cambridge Univ Press,
2016.
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| Colección: | London Mathematical Society lecture note series ;
437. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Series page; Title page; Copyright page; Contents; List of contributors; Preface; 1 Metric Diophantine Approximation: Aspects of Recent Work; 1.1 Background: Dirichlet and Bad; 1.2 Metric Diophantine Approximation: The Classical Lebesgue Theory; 1.3 Metric Diophantine Approximation: The Classical Hausdorff Theory; 1.4 The Higher-Dimensional Theory; 1.5 Ubiquitous Systems of Points; 1.6 Diophantine Approximation on Manifolds; 1.7 The Badly Approximable Theory; 2 Exponents of Diophantine Approximation; 2.1 Introduction and Generalities; 2.2 Further Definitions and First Results.
- 2.3 Overview of Known Relations Between Exponents2.4 Bounds for the Exponents of Approximation; 2.5 Spectra; 2.6 Intermediate Exponents; 2.7 Parametric Geometry of Numbers; 2.8 Real Numbers Which Are Badly Approximable by Algebraic Numbers; 2.9 Open Problems; 3 Effective Equidistribution of Nilflows and Bounds on Weyl Sums; 3.1 Introduction; 3.2 Nilflows and Weyl Sums; 3.3 The Cohomological Equation; 3.4 The Heisenberg Case; 3.5 Higher-Step Filiform Nilflows; 4 Multiple Recurrence and Finding Patterns in Dense Sets; 4.1 Szemerédi's Theorem and Its Relatives; 4.2 Multiple Recurrence.
- 4.3 Background from Ergodic Theory4.4 Multiple Recurrence in Terms of Self-Joinings; 4.5 Weak Mixing; 4.6 Roth's Theorem; 4.7 Towards Convergence in General; 4.8 Sated Systems and Pleasant Extensions; 4.9 Further Reading; 5 Diophantine Problems and Homogeneous Dynamics; 5.1 Equidistribution and the Gauss Circle Problem; 5.2 Counting Points in SL[sub(2)](Z) · i ⁶"H; 5.3 Dirichlet's Theorem and Dani's Correspondence; 6 Applications of Thin Orbits; 6.1 Lecture 1: Closed Geodesics, Binary Quadratic Forms, and Duke's Theorem.
- 6.2 Lecture 2: Three Problems in Continued Fractions: ELMV, McMullen, and Zaremba6.3 Lecture 3: The Thin Orbits Perspective; Index.