دانلود کتاب The Great Prime Number Race

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Cover Title page Preface Chapter 1. The Riemann zeta function 1.1. Introduction 1.2. The Riemann zeta function 1.3. The prime numbers 1.4. The Riemann zeta function 1.5. Euler and the zeta function 1.6. Meromorphic continuation of ?(?) Chapter 2. The Euler product 2.1. The zeta function and the Euler product 2.2. The logarithmic derivative of ?(?) Chapter 3. The functional equation 3.1. The gamma function 3.2. The functional equation 3.3. Some zeta values 3.4. Euler and the functional equation 3.5. The Euler constant revisited Chapter 4. The explicit formulas in analytic number theory 4.1. The von Mangoldt explicit formula 4.2. Can you hear the Riemann hypothesis? 4.3. Comparison with Fourier series 4.4. Proof of the von Mangoldt formula 4.5. The logarithmic integral ??(?) 4.6. The Riemann formula 4.7. Origin of the Riemann explicit formula Chapter 5. The prime number theorem 5.1. The Riemann-Ramanujan approximation 5.2. Proof of the prime number theorem Chapter 6. Oscillation of ?(?)-??(?) 6.1. Littlewood’s theorem 6.2. Lehman’s theorem Chapter 7. The prime number race 7.1. On the logarithmic density 7.2. Upper bounds for the Skewes number Chapter 8. Exercises, hints, and selected solutions 8.1. Exercises 8.2. Hints and selected solutions Bibliography Index Back Cover