Index

Abel summation formula, 5

Abscissa

of convergence, 76

of absolute convergence, 76

Arithmetic function,

additive, 85

multiplicative, 75

strongly additive, 85

strongly multiplicative, 75

totally additive, 85

totally multiplicative, 75

Artin constant, 257

Average order, 86

Asymptotic density, 11

Asymptotic mean value, 82

Bernoulli number, 4

Bernoulli polynomial, 4

Bertrand Postulate, 29

Brun-Titchmarsh theorem, 188

Buchstab identity, 135

Character, 235

Conjecture

abc, 167

Artin, 235

Bateman-Horn, 35

Carmichael, 109

Catalan, 171

Elliott-Halberstam, 253

Erd˝ os-Woods, 173

Goldbach, 192

k-abc, 175

Lehmer, 109

Prime k-tuples, 33

Twin prime, 31

Density of a set, 11

Dirichlet product, 79

Dirichlet series, 76

Elite prime, 228

Erd˝ os Multiplication Table Problem,

105

Euler constant, xiii

Formula

Euler-MacLaurin, 2

Legendre, 180

Stirling, 11

Wallis, 13

Function

Dickman, 134

distribution, 88

Euler, 115

largest prime factor, 131

M¨ obius, 56

number of divisors, 58

number of prime factors, 86

regularly varying, 8

Riemann Zeta, 39

slowly oscillating, 8

smallest prime factor, 127

von Mangoldt, 51

Functional equation, 71

413