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| Notation | |
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| Errata | |
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| Elementary Theory | |
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| Definition of [xi](s) and Elementary Properties | |
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| The Functional Equation | |
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| The Hadamard Product Formula | |
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| The Riemann-von Mangoldt Formula | |
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| An Approximate Functional Equation | |
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| Mean Value Theorems | |
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| Various Dirichlet Series Connected with [xi](s) | |
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| Other Zeta-Functions | |
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| Unproved Hypotheses | |
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| Exponential Integrals and Exponential Sums | |
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| Exponential Integrals | |
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| Exponential Sums | |
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| The Theory of Exponent Pairs | |
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| Two-Dimensional Exponent Pairs | |
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| The Voronoi Summation Formula | |
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| Introduction | |
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| The Truncated Voronoi Formula | |
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| The Weighted Voronoi Formula | |
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| Other Formulas of the Voronoi Type | |
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| The Approximate Functional Equations | |
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| The Approximate Functional Equation for [xi](s) | |
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| The Approximate Functional Equation for [xi superscript 2](s) | |
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| The Approximate Functional Equation for Higher Powers | |
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| The Reflection Principle | |
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| The Fourth Power Moment | |
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| Introduction | |
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| The Mean Value Theorem for Dirichlet Polynomials | |
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| Proof of the Fourth Power Moment Estimate | |
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| The Zero-free Region | |
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| A Survey of Results | |
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| The Method of Vinogradov-Korobov | |
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| Estimation of the Zeta Sum | |
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| The Order Estimate of [xi](s) Near [sigma] = 1 | |
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| The Deduction of the Zero-Free Region | |
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| Mean Value Estimates Over Short Intervals | |
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| Introduction | |
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| An Auxiliary Estimate | |
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| The Mean Square When [sigma] Is in the Critical Strip | |
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| The Mean Square When [sigma] = 1/2 | |
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| The Order of [xi](s) in the Critical Strip | |
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| Third and Fourth Power Moments in Short Intervals | |
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| Higher Power Moments | |
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| Introduction | |
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| Some Convexity Estimates | |
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| Power Moments for [sigma] = 1/2 | |
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| Power Moments for 1/2 [less than sign sigma less than sign] 1 | |
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| Asymptotic Formulas for Power Moments When 1/2 [less than sign sigma less than sign] 1 | |
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| Omega Results | |
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| Introduction | |
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| Omega Results When [sigma greater than or equal] 1 | |
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| Lemmas on Certain Order Results | |
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| Omega Results for 1/2 [less than or equal sigma less than or equal] 1 | |
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| Lower Bounds for Power Moments When [sigma] = 1/2 | |
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| Zeros on the Critical Line | |
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| Levinson's Method | |
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| Zeros on the Critical Line in Short Intervals | |
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| Consecutive Zeros on the Critical Line | |
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| Zero-Density Estimates | |
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| Introduction | |
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| The Zero-Detection Method | |
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| The Ingham-Huxley Estimates | |
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| Estimates for [sigma] Near Unity | |
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| Reflection Principle Estimates | |
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| Double Zeta Sums | |
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| Zero-Density Estimates for 3/4 [less than sign sigma less than sign] 1 | |
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| Zero-Density Estimates for [sigma] Close to 3/4 | |
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| The Distribution of Frimes | |
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| General Remarks | |
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| The Explicit Formula for [psi](x) | |
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| The Prime Number Theorem | |
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| The Generalized von Mangoldt Function and the Mobius Function | |
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| Von Mangoldt's Function in Short Intervals | |
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| The Difference between Consecutive Primes | |
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| Almost Primes in Short Intervals | |
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| Sums of Differences between Consecutive Primes | |
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| The Dirichlet Divisor Problem | |
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| Introduction | |
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| Estimates for [Delta subscript 2](x) and [Delta subscript 3](x) | |
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| Estimates of [Delta subscript k](x) by Power Moments of the Zeta-Function | |
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| Estimates of [Delta subscript k](x) When k Is Very Large | |
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| Estimates of [beta subscript k] | |
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| Mean-Square Estimates of [Delta subscript k](x) | |
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| Large Values and Power Moments of [Delta subscript k](x) | |
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| The Circle Problem | |
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| Various Other Divisor Problems | |
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| Summatory Functions of Arithmetical Convolutions | |
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| Some Applications of the Convolution Method | |
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| Three-Dimensional Divisor Problems | |
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| Powerful Numbers | |
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| Nonisomorphic Abelian Groups of a Given Order | |
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| The General Divisor Function d[subscript z](n) | |
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| Small Additive Functions | |
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| Atkinson's Formula for the Mean Square | |
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| Introduction | |
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| Proof of Atkinson's Formula | |
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| Modified Atkinson's Formula | |
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| The Mean Square of E(t) | |
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| The Connection Between E(T) and [Delta](x) | |
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| Large Values and Power Moments of E(T) | |
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| Appendix | |
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| References | |
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| Author Index | |
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| Subject Index | |