解析数论问题集

Preface to the Second Edition Acknowledgments for the Second Edition Preface to the First Edition Acknowledgments for the First Edition ⅠProblems 1 Arithmetic Functions 1.1 The Mobius Inversion Formula and Applications 1.2 Formal Dirichlet Series 1.3 Orders of Some Arithmetical Functions 1.4 Average Orders of Arithmetical Functions 1.5 Supplementary Problems 2 Primes in Arithmetic Progressions 2.1 Summation Techniques 2.2 Characters mod q 2.3 Dirichlet's Theorem 2.4 Dirichlet's Hyperbola Method 2.5 Supplementary Problems 3 The Prime Number Theorem 3.1 Chebyshev's Theorem 3.2 Nonvanishing of Dirichlet Series on Re(s) = 1 3.3 The Ikehara - Wiener Theorem 3.4 Supplementary Problems 4 The Method of Contour Integration 4.1 Some Basic Integrals 4.2 The Prime Number Theorem 4.3 Further Examples 4.4 Supplementary Problems 5 Functional Equations 5.1 Poisson's Summation Formula 5.2 The Riemann Zeta Function 5.3 Gauss Sums 5.4 Dirichlet L-functions 5.5 Supplementary Problems …… Ⅱ Solutions Reterences Index

《国外优秀数学著作原版系列：解析数论问题集（第2版）》是国外优秀数学著作原版系列之一，解析数论，为数论中的分支，它使用由数学分析中发展出的方法，作为工具，来解决数论中的问题。它首次出现在数学家狄利克雷使用数学分析方法证明狄利克雷定理。