Author(s): Roger Plymen
Series: Student Mathematical Library #92
Edition: 1
Publisher: American Mathematical Society
Year: 2020
Language: English
Commentary: This is just http://libgen.rs/book/index.php?md5=C80401BA4233964238C81C342C0A2019 , without the huge invisible graphic on page 1 (that has nothing to do with the book)
Pages: 138
City: Providence, RI
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
