Higher Order Fourier Analysis:Graduate Studies in Mathematics V.142

Higher Order Fourier Analysis:Graduate Studies in Mathematics V.142
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作者: ,
2012-10
ISBN: 9780821889862
装帧: 其他
页数: 187页
  • Preface                                                                                                                              ix
    Acknowledgements                                                                                                     x
    Chapter 1.  Higher order Fourier analysis                                                                   1
    §1.1.  Equidistribution of polynomial sequences in tori                                          2
    §1.2.  Roth's theorem                                                                                                  26
    §1.3.  Linear patterns                                                                                                  45
    §1.4.  Equidistibution of polynomials over finite fields                                          59
    §1.5.  The inverse conjecture for the Gowers norm I. The finite field case        74
    §1.6.  The inverse conjecture for the Gowers norm II. The integer case            92
    §1.7.  Linear equations in primes                                                                            109
    Chapter 2.  Related articles                                                                                        129
    §2.1.  Ultralimit analysis and quantitative algebraic geometry                          130
    §2.2.  Higher order Hilbert spaces                                                                          149
    §2.3.  The uncertainty principle                                                                               162
    Bibliography                                                                                                                  179
    Index                                                                                                                               185
  • 目录:
    Preface                                                                                                                              ix
    Acknowledgements                                                                                                     x
    Chapter 1.  Higher order Fourier analysis                                                                   1
    §1.1.  Equidistribution of polynomial sequences in tori                                          2
    §1.2.  Roth's theorem                                                                                                  26
    §1.3.  Linear patterns                                                                                                  45
    §1.4.  Equidistibution of polynomials over finite fields                                          59
    §1.5.  The inverse conjecture for the Gowers norm I. The finite field case        74
    §1.6.  The inverse conjecture for the Gowers norm II. The integer case            92
    §1.7.  Linear equations in primes                                                                            109
    Chapter 2.  Related articles                                                                                        129
    §2.1.  Ultralimit analysis and quantitative algebraic geometry                          130
    §2.2.  Higher order Hilbert spaces                                                                          149
    §2.3.  The uncertainty principle                                                                               162
    Bibliography                                                                                                                  179
    Index                                                                                                                               185
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