604 Index
correspondence, 4
open
ball, 28, 33, 342
set, 28, 43
operations research, 78
Oppenheim’s conjecture, 324, 325
order in natural numbers, 8
order of
element, 59, 113, 114
group, 57, 109, 113, 114
Hadamard matrix, 230
pole, 48
projective plane, 248
ordered field, 23, 26, 41, 76, 79, 280,
296–297, 308
ordinary differential equation, 36–38,
76, 510
orientation, 225, 347
Ornstein’s theorem, 483
orthogonal
basis, 74, 294, 335
complement, 293
group, 440
matrix, 52, 238
set, 73
sum, 293, 349
vectors, 73, 293
orthogonality relations, 402, 415–416,
418, 437
orthonormal set, 73–75
Oseledets ergodic theorem, 489
Ostrowski’s theorems, 266, 284, 290,
313
packing, 337, 359–360
p-adic
absolute value, 262
integer, 275, 277, 287
number, 18, 271, 275, 277, 287, 288,
310, 313, 436
pair correlation conjecture, 383–384,
395
Paley’s construction, 231–233, 255, 350
parallelogram law, 73, 79, 561, 564
parallelotope, 229, 333
parametrization, 51–52, 217, 219,
554–555, 558, 574
Parseval’s equality, 74–75, 335–336
partial
fractions, 497
order, 85
quotient, 181, 190, 212, 480
partition of
positive integer, 544–549
set, 4, 58
partition theory, texts, 581
Pascal triangle, 94
path-connected, 44, 437, 441
Peano axioms, 5, 76
Pell equation, 144, 196–201, 217
for polynomials, 213, 219
pendulum, period of, 494
P ́epin test, 160–161
percolation processes, 489
perfect number, 157–159, 175
period of continued fraction, 192–194,
197–199, 217
periodicity of
continued fraction, 192–194, 209, 217
elliptic functions, 513–516, 527, 538
exponential function, 46–47
permutation, 57, 129–131, 227
perpendicular, 73
Perron–Frobenius theorem, 480
Pfister’s multiplicative forms, 323
pi(π), 46, 48, 186, 217, 222, 364, 509
Picard’s theorem, 538
pigeonhole principle, 10, 57
Plancherel theorem, 435
Poincar ́e
model, 208, 219
recurrence theorem, 483–484
point, 247, 250, 549, 550
at infinity, 550, 552, 553
pointwise ergodic theorem, 466
Poisson summation, 138, 378, 394, 435,
538
polar
coordinates, 47, 495
lattice, 334
pole of ordern,48
poles of elliptic functions, 526–527
polynomial, 96–103