598 Index
Fermat number, 160–161, 175
Fermat prime, 160–161
Fermat’s
last theorem, 151–152, 175, 579–
580, 584
little theorem, 110–112, 116
Fibonacci numbers, 95
field, 23, 40, 62–63, 109, 125
of fractions, 88, 100, 261
field theory, texts, 79
finite
dimensional, 66, 67
field, 109, 125, 232, 289, 298, 386–
387, 570–571
field extension, 45, 67, 283–284, 288,
386
group, 57
set, 10
finitely generated, 63, 66, 95, 168, 172,
176, 559
Fischer’s inequality, 239, 243
fixed point, 32, 35, 37
theorems, 32, 76
flex, 551–553, 557
flow, 465, 481, 483
formal
derivative, 103, 112, 278
Laurent series, 211, 219, 263, 271,
289, 358
power series, 96, 124, 275, 287
Fourier
integrals, 435–436, 443
inversion formula, 435–436
series, 79, 138, 378, 436, 443, 450
transform, 374, 378, 435–436
fraction, 15
fractional part, 448, 479
free
action, 218
product, 203
subgroup, 172, 569
submodule, 172
Fresnel integral, 139
Frobenius
complement, 429
conjectures, 124, 211
group, 429, 443
kernel, 429
reciprocity theorem, 420
theorem on division rings, 69
Fuchsian group, 218
function, 4; 386
function fields, 386–388, 395
and coding theory, 388, 395
functional equation of
L-functions, 409, 443, 572
zeta functions, 380–381, 385, 387,
443
fundamental
domain, 203, 333, 346, 499
sequence, 25, 26, 30–33, 269, 270,
274
solution, 197–201
fundamental theorem of
algebra, 42–45, 69, 77, 98, 413
arithmetic, 88–90, 124, 145
Furstenberg’s theorems, 484–487, 490
Furstenberg–Katznelson theorem, 485
Furstenberg–Weiss theorem, 485Galois theory, 79, 160
gamma function, 328, 379–380, 394,
572
Gauss
class number problem, 218, 578, 584
invariant measure, 479
map, 479–480, 483, 489
sum, 135–140, 174
Gauss–Kuz’min theorem, 480, 489
Gaussian integer, 119–120, 141, 145,
542
Gaussian unitary ensemble, 384
GCDdomain, 87–90, 98, 100–101
gear ratios, 187
Gelfand–Raikov theorem, 434
general linear group, 68, 251, 440
generalized
character, 428
trigonometric polynomial, 75, 458
upper half-plane, 218–219
generated by, 59, 60, 63, 66, 91, 114,
161, 331, 465
generating function, 544, 581