606 Index
non-residue, 112–113, 121, 129,
132–133, 385
polynomial, 42, 283
residue, 112–113, 121, 129,
132–133, 280
space, 292–303, 324
quadratic spaces, texts, 324
quantum group, 582
quartic polynomial, 76–77
quasicrystal, 359
quasiperiodic tiling, 359
quaternion, 48–53, 69, 77–82, 120–122,
541
quaternionic analysis, 77
Quillen–Suslin theorem, 176
quotient, 15, 48, 90
group, 58
ring, 63, 107, 384
space, 209, 210, 218
R ̊adstr ̈om’s cancellation law, 353, 360
Ramanujan’s tau-function, 388, 395
random matrices, 384, 395, 489
range of linear map, 68
rank of
elliptic curve, 569–570, 572
linear map, 68
rational
function, 88, 212, 262, 386
number, 15–17, 181–182, 277
transformation, 558
real
analysis, 26, 76
number, 22–26
part, 40
quadratic field, 140
reciprocal lattice, 334
reciprocity for Gauss sums, 137
recurrence for number of partitions, 545
recursion theorem, 5–6
reduced
automorphism group, 252
lattice basis, 358
quadratic form, 206, 207
quadratic irrational, 192–194
reducible
curve, 551
polynomial, 282
representation, 411
Reed–Muller code, 255–256
refinement theorems, 86, 123–124
reflection, 53, 300
reflexive relation, 4
regular prime, 151
regular representation, 410, 416–417,
434, 437
relatively
dense set, 343
prime, 85, 167
relevant vector, 344
remainder, 90
theorem, 99
replacement laws, 106
representation of
compact group, 436–439
finite group, 410–413, 437, 443
group, 410, 442–444
locally compact group, 434–436
representative of
coset, 58, 78
residue field, 276
representatives, distinct, 78
represented by quadratic form, 294, 295
residue, 48, 371, 390
class, 107, 400
field, 274–276, 386
resolution of singularities, 558
restriction of map, 4
Ribet’s theorem, 580
Riemann
integrable, 327, 358, 449, 450, 452
normal form, 498–502, 510,
555–556
surface, 218
zeta function, 366, 370–373,
380–384, 390–392, 394
Riemann hypothesis, 381–383, 391–392,
395, 398
for algebraic varieties, 388, 395
for elliptic curves, 571, 574, 583
for function fields, 387–388, 395,
583
Riemann–Lebesgue lemma, 376