Index 593arithmetic-geometric mean, 502–509,
512, 535–536
arithmetical function, 152–154, 175
arithmetical functions, 153, 175
Artin’s
primitive root conjecture, 124–125,
385, 388
reciprocity law, 174
associative, 4, 60
algebra, 68–69, 78, 79
law, 7, 55, 83
asymptote, 550
automorphism group of
code, 255
Hadamard matrix, 252
t-design, 250
automorphism of
H,O,77
group, 59
Hadamard matrix, 252
quadratic field, 140
ring, 64
torus, 473
badly approximable number, 190, 194,
217, 463, 489
Baire’s category theorem, 487
Baker’s theorem, 583
baker’s transformation, 482
balanced incomplete block design, 247
Banach algebra, 434
basis of
lattice, 332, 333
module, 164, 169, 173
vector space, 66
Bateman–Horn conjecture, 393–395
Beal’s conjecture, 581
Bernoulli number, 151
Bernoulli shift, one-sided, 479, 483
Bernoulli shift, two-sided, 477, 483
Bernstein’s theorem, 394
Bertrand’s postulate, 366
Bessel’s inequality, 74
best approximation
in inner product space, 73
of real number, 186, 217
beta integral, 380
B ́ezout
domain, 95, 101, 124, 168
identity, 91,92, 109, 118, 121, 167
Bieberbach’s theorems, 346, 358
bijection, 4
bijective map, 4, 10
binary
digit (‘bit’), 255
linear code, 255, 256
operation, 55, 60
quadratic form, 205–207, 218
relation, 3
binomial
coefficient, 92–94, 111
theorem, 110, 116, 537
birational
equivalence, 216, 558, 575, 582
transformation, 216, 558
Birkhoff’s
ergodic theorem, 464–471, 479, 489
recurrence theorem, 485
Blaschke’s selection principle, 353,
356, 357, 360
Blichfeldt’s theorem, 334
block, 247, 250
Bohl’s theorem, 448, 451, 458
Bolzano–Weierstrass theorem, 25, 42
Boolean algebra, 75–76
Boolean ring, 61
Borel subset, 472, 473, 479, 481
bounded
sequence, 24, 26
set, 30
variation, 461–462, 489
bracket product, 440
Brahmagupta’s identity, 195–196, 304
Brauer group, 324
Brauer’s theorem, 425
Brouwer’s fixed point theorem, 76
Bruck–Ryser–Chowla theorem, 249,
321, 325
Brun’s theorem, 392, 395
BSDconjecture, 570, 572–573, 578,
583
Burnside’s theorem, 427–428calendars, 119, 187