Dynamics and analytic number theory

Dynamics and analytic number theory

by Badziahin, Dmitry, (Dmitry A.)

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Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.

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Title Statements

  • Full title :Dynamics and analytic number theory.

Summary

Presents current research in various topics, including homogeneous dynamics, Diophantine approximation and combinatorics.

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Edition Statements

  • Publication Date:2016.

Publication Statements

  • Publisher(s):Cambridge Univ. Press
  • Place of Publication:Place of publication not identified
  • Language:eng
  • Publication Date:2016.

The Physical Object

  • Description:1 online resource

Edition Identifiers

  • ISBN:9781316402696, 131640269X, 9781316818855, 1316818853
  • oclc:ocn962437687
  • LC Classification:QA241
  • Dewey Decimal:512.7

Table of Contents

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 f…

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Subjects

Conference papers and proceedings Dynamics Dynamics -- Congresses Dynamique -- Congrès MATHEMATICS -- Algebra Number theory Number theory -- Congresses Théorie des nombres -- Congrès

Writers

Badziahin, Dmitry, (Dmitry A.)

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