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
