Index Additive function, 3 Arithmetic function, 3 Critical line, 34, 55 Critical strip, 30 Dirichlet convolution, 3 Dirichlet polynomial, 47 square mean value, 47 Dirichlet series, 3 Divisor function, 5 Euler constant, 23 Euler ϕ-function, 5 Euler-Maclaurin formula, 9 Function of finite order, 27 Γ-function, 115 Jensen’s formula, 28 Kloosterman sums, 101 Levinson-Littlewood shift parameter, 109 Liouville function, 5 M¨ obius function, 4 M¨ obius inversion, 4 Mertens formulas, 14 Multiplicative function, 3 Natural numbers, 3 Perron’s formula, 37 Poisson formula, 25 Prime Number Theorem, 15 Prime numbers, 3 Riemann Hypothesis, vii, 21, 55–57 Riemann zeta-function, vii, 4, 21 convexity bound, 44 critical zeros, 57 fourth power moment, 51 functional equation, 21, 26 mollified, 55 non-trivial zeros, 21 trivial zeros, 21 Stirling’s formulas, 115 Theta series, 25 von Mangoldt function, 6 well-spaced points, 52 119

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