Riemann's Zeta Function

✍ Scribed by H.M. Edwards

Publisher: Academic Press, Elsevier
Year: 1974
Leaves: 321
Series: Pure and Applied Mathematics 58
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

Superb study of one of the most influential classics in mathematics examines the landmark 1859 publication entitled On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics.

✦ Table of Contents

Content:
Editorial Page
Page iii

Copyright Page
Page iv

Preface
Pages ix-xi

Acknowledgments
Page xiii

Chapter 1 Riemann's Paper
Pages 1-38

Chapter 2 The Product Formula for ξ
Pages 39-47

Chapter 3 Riemann's Main Formula
Pages 48-67

Chapter 4 The Prime Number Theorem
Pages 68-77

Chapter 5 De la Vallée Poussin's Theorem
Pages 78-95

Chapter 6 Numerical Analysis of the Roots by Euler-MacIaurin Summation
Pages 96-135

Chapter 7 The Riemann-Siegal Formula
Pages 136-170

Chapter 8 Large-Scale Computations
Pages 171-181

Chapter 9 The Growth of Zeta as t → ∞ and the Location of Its Zeros
Pages 182-202

Chapter 10 Fourier Analysis
Pages 203-225

Chapter 11 Zeros on the line
Pages 226-259

Chapter 12 Miscellany
Pages 260-298

Appendix on the Number of Primes Less Than a Given Magnitude Original Research Article
Pages 299-305
Bernhard Riemann

References
Pages 306-310

Index
Pages 311-315

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