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| Introduction to the Riemann Hypothesis | |
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| Why This Book | |
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| The Holy Grail | |
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| Riemann's Zeta and Liouville's Lambda | |
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| The Prime Number Theorem | |
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| Analytic Preliminaries | |
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| The Riemann Zeta Function | |
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| Zero-free Region | |
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| Counting the Zeros of [zeta](s) | |
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| Hardy's Theorem | |
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| Algorithms for Calculating [zeta](s) | |
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| Euler-MacLaurin Summation | |
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| Backlund | |
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| Hardy's Function | |
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| The Riemann-Siegel Formula | |
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| Gram's Law | |
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| Turing | |
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| The Odlyzko-Schonhage Algorithm | |
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| A Simple Algorithm for the Zeta Function | |
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| Further Reading | |
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| Empirical Evidence | |
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| Verification in an Interval | |
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| A Brief History of Computational Evidence | |
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| The Riemann Hypothesis and Random Matrices | |
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| The Skewes Number | |
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| Equivalent Statements | |
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| Number-Theoretic Equivalences | |
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| Analytic Equivalences | |
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| Other Equivalences | |
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| Extensions of the Riemann Hypothesis | |
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| The Riemann Hypothesis | |
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| The Generalized Riemann Hypothesis | |
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| The Extended Riemann Hypothesis | |
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| An Equivalent Extended Riemann Hypothesis | |
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| Another Extended Riemann Hypothesis | |
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| The Grand Riemann Hypothesis | |
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| Assuming the Riemann Hypothesis and Its Extensions | |
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| Another Proof of The Prime Number Theorem | |
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| Goldbach's Conjecture | |
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| More Goldbach | |
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| Primes in a Given Interval | |
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| The Least Prime in Arithmetic Progressions | |
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| Primality Testing | |
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| Artin's Primitive Root Conjecture | |
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| Bounds on Dirichlet L-Series | |
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| The Lindelof Hypothesis | |
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| Titchmarsh's S(T) Function | |
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| Mean Values of [zeta](s) | |
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| Failed Attempts at Proof | |
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| Stieltjes and Mertens' Conjecture | |
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| Hans Rademacher and False Hopes | |
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| Turan's Condition | |
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| Louis de Branges's Approach | |
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| No Really Good Idea | |
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| Formulas | |
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| Timeline | |
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| Original Papers | |
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| Expert Witnesses | |
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| E. Bombieri (2000-2001) | |
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| P. Sarnak (2004) | |
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| J. B. Conrey (2003) | |
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| A. Ivic (2003) | |
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| The Experts Speak for Themselves | |
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| P. L. Chebyshev (1852) | |
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| B. Riemann (1859) | |
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| J. Hadamard (1896) | |
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| C. de la Vallee Poussin (1899) | |
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| G. H. Hardy (1914) | |
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| G. H. Hardy (1915) | |
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| G. H. Hardy and J. E. Littlewood (1915) | |
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| A. Weil (1941) | |
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| P. Turan (1948) | |
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| A. Selberg (1949) | |
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| P. Erdos (1949) | |
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| S. Skewes (1955) | |
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| C. B. Haselgrove (1958) | |
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| H. Montgomery (1973) | |
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| D. J. Newman (1980) | |
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| J. Korevaar (1982) | |
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| H. Daboussi (1984) | |
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| A. Hildebrand (1986) | |
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| D. Goldston and H. Montgomery (1987) | |
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| M. Agrawal, N. Kayal, and N. Saxena (2004) | |
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| References | |
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| References | |
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| Index | |