The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike (CMS Books in Mathematics)

Contents
Part I: Introduction to the Riemann Hypothesis
	1. Why This Book
		1.1 The Holy Grail
		1.2 Riemann\'s Zeta and Liouville\'s Lambda
		1.3 The Prime Number Theorem
	2. Analytic Preliminaries
		2.1 The Riemann Zeta Function
		2.2 Zero-free Region
		2.3 Counting the Zeros of ζ(s)
		2.4 Hardy\'s Theorem
	3. Algorithms for Calculating ζ(s)
		3.1 Euler–MacLaurin Summation
		3.2 Backlund
		3.3 Hardy\'s Function
		3.4 The Riemann–Siegel Formula
		3.5 Gram\'s Law
		3.6 Turing
		3.7 The Odlyzko–Schönhage Algorithm
		3.8 A Simple Algorithm for the Zeta Function
		3.9 Further Reading
	4. Empirical Evidence
		4.1 Verification in an Interval
		4.2 A Brief History of Computational Evidence
		4.3 The Riemann Hypothesis and Random Matrices
		4.4 The Skewes Number
	5. Equivalent Statements
		5.1 Number-Theoretic Equivalences
		5.2 Analytic Equivalences
		5.3 Other Equivalences
	6. Extensions of the Riemann Hypothesis
		6.1 The Riemann Hypothesis
		6.2 The Generalized Riemann Hypothesis
		6.3 The Extended Riemann Hypothesis
		6.4 An Equivalent Extended Riemann Hypothesis
		6.5 Another Extended Riemann Hypothesis
		6.6 The Grand Riemann Hypothesis
	7. Assuming the Riemann Hypothesis and Its Extensions
		7.1 Another Proof of The Prime Number Theorem
		7.2 Goldbach\'s Conjecture
		7.3 More Goldbach
		7.4 Primes in a Given Interval
		7.5 The Least Prime in Arithmetic Progressions
		7.6 Primality Testing
		7.7 Artin\'s Primitive Root Conjecture
		7.8 Bounds on Dirichlet L-Series
		7.9 The Lindelöf Hypothesis
		7.10 Titchmarsh\'s S(T) Function
		7.11 Mean Values of ζ(s)
	8. Failed Attempts at Proof
		8.1 Stieltjes and Mertens\' Conjecture
		8.2 Hans Rademacher and False Hopes
		8.3 Turán\'s Condition
		8.4 Louis de Branges\'s Approach
		8.5 No Really Good Idea
	9. Formulas
	10. Timeline
Part II: Original Papers
	11. Expert Witnesses
		11.1 E. Bombieri (2000–2001)
		11.2 P. Sarnak (2004)
		11.3 J. B. Conrey (2003)
		11.4. A. Ivić (2003)
	12. The Experts Speak for Themselves
		12.1 P. L. Chebyshev (1852)
		12.2 B. Riemann (1859)
		12.3 J. Hadamard (1896)
		12.4 C. de la Vallée Poussin (1899)
		12.5 G. H. Hardy (1914)
		12.6 G. H. Hardy (1915)
		12.7 G. H. Hardy and J. E. Littlewood (1915)
		12.8 A. Weil (1941)
		12.9 P. Turán (1948)
		12.10 A. Selberg (1949)
		12.11 P. Erdös (1949)
		12.12 S. Skewes (1955)
		12.13 C. B. Haselgrove (1958)
		12.14 H. Montgomery (1973)
		12.15 D. J. Newman (1980)
		12.16 J. Korevaar (1982)
		12.17 H. Daboussi (1984)
		12.18 A. Hildebrand (1986)
		12.19 D. Goldston and H. Montgomery (1987)
		12.20 M. Agrawal, N. Kayal, and N. Saxena (2004)
References
References
Index
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	B
	C
	D
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	H
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	Q
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	Z