Hardy-Littlewood方法（第2版）（英文版）
内容提要 ：
There have been two earlier Cambridge Tracts that have touched upon the Hardy-Littlewood method, namely those of Landau, 1937, and Estermann, 1952. However there has been no general account of the method published in the United Kingdom despite the not inconsiderable contribution of English scholars in inventing and developing the method and the numerous monographs that have appeared abroad. The purpose of this tract is to give an account of the classical forms of the method together with an outline of some of the more recent developments. It has been deemed more desirable to have this particular emphasis as many of the later applications make important use of the classical material.
编辑推荐 ：
There have been two earlier Cambridge Tracts that have touched upon the Hardy-Littlewood method, namely those of Landau, 1937, and Estermann, 1952. However there has been no general account of the method published in the United Kingdom despite the not inconsiderable contribution of English scholars in inventing and developing the method and the numerous monographs that have appeared abroad. The purpose of this tract is to give an account of the classical forms of the method together with an outline of some of the more recent developments. It has been deemed more desirable to have this particular emphasis as many of the later applications make important use of the classical material.
本书为英文版。 目录 ：
Contents
Preface Preface to second edition Notation 1 Introduction and historical background 1.1 Waring's problem 1.2 The Hardy-Littlewood method 1.3 Goldbach's problem 1.4 Other problems 1.5 Exercises 2 The simplest upper bound for G(k) 2.1 The definition ofmajor and minor arcs 2.2 Auxiliary lemmas 2.3 The treatment of the minor arcs 2.4 The major arcs 2.5 The singular integral 2.6 The singular series 2.7 Summary 2.8 Exercises 3 Goldbach's problems 3.1 The ternary Goldbach problem 3.2 The binary Goldbach problem 3.3 Exercises 4 The major arcs in Waring's problem 4.1 The generating function 4.2 The exponential sum S(q, a) 4.3 The singular series 4.4 The contribution from the major arcs 4.5 The congruence condition 4.6 Exercises 5 Vinogradov's methods 5.1 Vinogradov's mean value theorem 5.2 The transition from the mean 5.3 The minor arcs in Waring's problem 5.4 An upper bound for G(k) 5.5 Wooley's refinement of Vinogradov's mean value theorem 5.6 Exercises 6 Davenport's methods 6.1 Sets ofsums of kth powers 6.2 G(4) = 16 6.3 Davenport's bounds for G(5) and G(6) 6.4 Exercises 7 Vinogradov's upper bound for G(k) 7.1 Some remarks on Vinogradov's mean value theorem 7.2 Preliminary estimates 7.3 An asymptotic formula for J(X) 7.4 Vinogradov's upper bound for G(k) 7.5 Exercises 8 A ternary additive problem 8.1 A general conjecture 8.2 Statement of the theorem 8.3 Definition of major and minor arcs 8.4 The treatment of n 8.5 The major arcs y(q.a) 8.6 The singular series 8.7 Completion of the proof of Theorem 8. 8.8 Exercises 9 Homogeneous equations and Birch's theorem …… 10 A theorem of Roth 11 Diophantine inequalities 12 Wooley's upper bound for G(k) Bibliography Index 前言：
There have been two earlier Cambridge Tracts that have touched upon the Hardy-Littlewood method, namely those of Landau, 1937, and Estermann, 1952. However there has been no general account of the method published in the United Kingdom despite the not inconsiderable contribution of English scholars in inventing and developing the method and the numerous monographs that have appeared abroad.
The purpose of this tract is to give an account of the classical forms of the method together with an outline of some of the more recent developments...
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