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