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解析数论导论txt，chm，pdf，epub，mobi下载作者: 阿波斯托尔 出版社: 世界图书出版公司 出版年: 2012-1 页数: 338 定价: 45.00元 丛书: Undergraduate Texts in Mathematics ISBN: 9787510040627 内容简介 · · · · · ·《解析数论导论》前五章讲述可约性、收敛和算术函数等基本概念。紧下来的章节讲述序列中素数的狄利克莱定理、高斯和、二次剩余、狄利克莱级数和欧拉积及其在黎曼zeta函数和狄利克莱函数中的应用，并且引进了划分的概念。书中每章末都收集了大量练习。前十章，除去第一章，任何具备基本微积分知识的人都可以读懂；最后四章需要对复函数理论（包括复积分和留数积分）一定的了解。 目录 · · · · · ·Historical IntroductionChapter 1The Fundamental Theorem of Arithmetic1.1 Introduction1.2 Divisibility1.3 Greatest common divisor1.4 Prime numbers1.5 The fundamental theorem of arithmetic1.6 The series of reciprocals of the primes1.7 The Euclidean algorithm1.8 The greatest common divisor of more than two, numbers Exercises for Chapter 1Chapter 2Arithmetical Functions and Dirichlet Multiplication2.1 Introduction2.2 The M6bius function (n)2.3 The Euler totient function (n)2.4 A relation connecting and u2.5 A product formula for (n)2.6 The Dirichlet product of arithmetical functions2.7 Dirichlet inverses and the M6bius inversion formula2.8 The Mangoldt function A(n)2.9 Muitiplicative functions2.10 Multiplicative functions and Dirichlet multiplication2.11 The inverse of a completely multiplicative function2.12 Liouville's function)2.13 The divisor functions a,(n)2.14 Generalized convolutions2.15 Formal power series2.16 The Bell series of an arithmetical function2.17 Bell series and Dirichlet multiplication2.18 Derivatives of arithmetical functions2.19 The Selberg identity Exercises for Chapter 2Chapter 3Averages of Arithmetical Functions3.1 Introduction3.2 The big oh notation. Asymptotic equality of functions3.3 Euler's summation formula3.4 Some elementary asymptotic formulas3.5 The average order of din)3.6 The average order of the divisor functions a,(n)3.7 The average order of ~0(n)3.8 An application to the distribution of lattice points visible from the origin3.9 The average order of/4n) and of A(n)3.10 The partial sums ofa Dirichlet product3.11 Applications to pin) and A(n)3.12 Another identity for the partial gums of a Dirichlet product Exercises for Chapter 3Chapter 4Some Elementary Theorems on the Distribution of PrimeNumbers4.1 Introduction4.2 Chebyshev's functions (x) and (x)4.3 Relations connecting/x) and n(x)4.4 Some equivalent forms of the prime number theorem4.5 Inequalities for (n) and p,4.6 Shapiro's Tauberian theorem4.7 Applications of Shapiro's theorem4.8 An asymptotic formula for the partial sums, (I/p)4.9 The partial sums of the M6bius function 914.10 Brief sketch of an elementary proof of the prime number theorem4.11 Selbcrg's asymptotic formula Exercises for Chapter 4Chapter 5Congruences 5.1 Definition and basic properties of congruences 5.2 Residue classes and complete residue systems 5.3 Linear congruencesChapter 6Finite Abelian Groups and Their CharactersChapter 7Dirichlet's Theorem on Primes in Arithmetic ProgressionsChapter 8Periodic Arithmetical Functions and Gauss SumsChapter 9Quadratic Residues and the Quadratic Reciprocity LawChapter 10Primitive RootsChapter 11Dirichlet Series and Euler ProductsChapter 12The Functions (s) and L(s,x)Chapter 13Analytic Proof of the Prime Number TheoremHistorical IntroductionChapter 1The Fundamental Theorem of Arithmetic1.1 Introduction1.2 Divisibility1.3 Greatest common divisor1.4 Prime numbers1.5 The fundamental theorem of arithmetic1.6 The series of reciprocals of the primes1.7 The Euclidean algorithm1.8 The greatest common divisor of more than two, numbers Exercises for Chapter 1Chapter 2Arithmetical Functions and Dirichlet Multiplication2.1 Introduction2.2 The M6bius function (n)2.3 The Euler totient function (n)2.4 A relation connecting and u2.5 A product formula for (n)2.6 The Dirichlet product of arithmetical functions2.7 Dirichlet inverses and the M6bius inversion formula2.8 The Mangoldt function A(n)2.9 Muitiplicative functions2.10 Multiplicative functions and Dirichlet multiplication2.11 The inverse of a completely multiplicative function2.12 Liouville's function)2.13 The divisor functions a,(n)2.14 Generalized convolutions2.15 Formal power series2.16 The Bell series of an arithmetical function2.17 Bell series and Dirichlet multiplication2.18 Derivatives of arithmetical functions2.19 The Selberg identity Exercises for Chapter 2Chapter 3Averages of Arithmetical Functions3.1 Introduction3.2 The big oh notation. Asymptotic equality of functions3.3 Euler's summation formula3.4 Some elementary asymptotic formulas3.5 The average order of din)3.6 The average order of the divisor functions a,(n)3.7 The average order of ~0(n)3.8 An application to the distribution of lattice points visible from the origin3.9 The average order of/4n) and of A(n)3.10 The partial sums ofa Dirichlet product3.11 Applications to pin) and A(n)3.12 Another identity for the partial gums of a Dirichlet product Exercises for Chapter 3Chapter 4Some Elementary Theorems on the Distribution of PrimeNumbers4.1 Introduction4.2 Chebyshev's functions (x) and (x)4.3 Relations connecting/x) and n(x)4.4 Some equivalent forms of the prime number theorem4.5 Inequalities for (n) and p,4.6 Shapiro's Tauberian theorem4.7 Applications of Shapiro's theorem4.8 An asymptotic formula for the partial sums, (I/p)4.9 The partial sums of the M6bius function 914.10 Brief sketch of an elementary proof of the prime number theorem4.11 Selbcrg's asymptotic formula Exercises for Chapter 4Chapter 5Congruences 5.1 Definition and basic properties of congruences 5.2 Residue classes and complete residue systems 5.3 Linear congruencesChapter 6Finite Abelian Groups and Their CharactersChapter 7Dirichlet's Theorem on Primes in Arithmetic ProgressionsChapter 8Periodic Arithmetical Functions and Gauss SumsChapter 9Quadratic Residues and the Quadratic Reciprocity LawChapter 10Primitive RootsChapter 11Dirichlet Series and Euler ProductsChapter 12The Functions (s) and L(s,x)Chapter 13Analytic Proof of the Prime Number Theorem · · · · · · () |
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