目录 Preface Introduction Chapter 1. Arithmetic Functions 1.1. Notation and definitions 1.2. Generating series 1.3. Dirichlet convolution 1.4. Examples 1.5. Arithmetic functions on average 1.6. Sums of multiplicative functions 1.7. Distribution of additive functions Chapter 2. Elementary Theory of Prime Numbers 2.1. The Prime Number Theorem 2.2. Tchebyshev method 2.3. Primes in arithmetic progressions 2.4. Reflections on elementary proofs of the Prime Number Theorem Chapter 3. Characters 3.1. Introduction 3.2. Dirichlet characters 3.3. Primitive characters 3.4. Gauss sums 3.5. Real characters 3.6. The quartic residue symbol 3.7. The Jacobi-Dirichlet and the Jacobi-Kubota symbols 3.8. Hecke characters Chapter 4. Summation Formulas $4.1. Introduction 4.2. The Euler-Maclaurin formula 4.3. The Poisson summation formula 4.4. Summation formulas for the ball 4.5. Summation formulas for the hyperbola 4.6. Functional equations of Dirichlet L-functions 4.A. Appendix: Fourier integrals and series Chapter 5. Classical Analytic Theory of L-functions 5.1. Definitions and preliminaries 5.2. Approximations to L-functions 5.3. Counting zeros of L-functions 5.4. The zero-free region 5.5. Explicit formula 5.6. The prime number theorem 5.7. The Grand Riemann Hypothesis 5.8. Simple consequences of GRH 5.9. The Riemann zeta function and Dirichlet L-functions 5.10. L-functions of number fields 5.11. Classical automorphic L-functions 5.12. General automorphic L-functions 5.13. Artin L-functions 5.14. L-functions of varieties 5.A. Appendix: complex analysis Chapter 6. Elementary Sieve Methods 6.1. Sieve problems
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