Index
Ψ(x, y), 11, 115, 206
upper bound for Ψ(x, log x), 257
γ, 98
Li(x), 86
and , xiii
ω(n) and Ω(n), 111
π(x), 1
σ−1(n), 254
∼, xiii
ζ(s), 4


163,
32
f-nomial period, see also Gaussian period
m-gonal number, 148
s(n), 248
abundant numbers, 248
density, 251
aliquot sequence, 252
geometric growth, 263, 268
almost prime, 168
amicable numbers, 252
Artin’s constant, 245
Bertrand’s postulate, 89, 94, 108
Besicovitch set, 276
big-Oh notation, xii, xiii
Bombieri–Vinogradov theorem, 109
Bonferroni inequalities, 177
Brun’s constant, 180
Brun’s method, 206
Brun’s pure sieve, 168, 175
application to estimating π2(x), 179
general version, 178
working version, 178
Brun–Hooley sieve, 168, 182
application to sums of primes
(Schnirelmann’s theorem), 196
application to the generalized twin prime
problem, 190, 196
application to the Goldbach problem,
185, 193
lower bound method, 191
upper bound method, 183
Brun–Titchmarsh inequality, 206, 245, 273
Carath´ eodory’s theorem, 156
Cardano’s formula, 71
Catalan–Dickson conjecture, 253
character of a finite abelian group, 123
characters of
(Z/mZ)×,
124
classification of characters, 124
orthogonality relations, 125, 142
trivial character, 123
Chebotarev density theorem, 26, 40
Chebyshev’s theorems, 89, 92, 217, 220
class number 1 problem, 22
cluster prime, 204
composite numbers, 1
of the form α · n! + 1, 31
of the form
ξαn
, 33
constructibility
of regular 17-gon, 45, 56, 78
of regular n-gon (Gauss–Wantzel
characterization), 46, 55
rudiments, 50
constructible number, 51, 77
cubic reciprocity law (Eisenstein), 75
cubic reciprocity law (Jacobi), 50, 64, 70,
82
form of Z.-H. Sun, 73
cubic residuacity
301
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