602 Index
subgroup, 441
limit, 24, 30, 269
linear
code, 255, 388
combination, 65
differential system, 172–173
Diophantine equation, 91, 161,
165–166
fractional transformation, 179, 208,
500, 531, 535
map, 67
systems theory, 176
transformation, 67
linear algebra, texts, 79
linearly dependent, 66
linearly independent, 66
Linnik’s theorem, 409
Liouville’s
integration theory, 537
theorem in complex analysis, 77, 517
theorem in mechanics, 481
Lipschitz condition, 460
Littlewood’s theorem, 383, 395
LLL-algorithm, 358
L^2 -norm, 72
local-global principle, 317–318, 325
locally compact, 28
group, 358, 432–436, 444, 490
topological space, 432
valued field, 284–290
locally Euclidean topological space, 440
logarithm, 39, 364
lower
bound, 14, 19, 22
limit, 24
triangular matrix, 229
Lucas–Lehmer test, 158, 175
Mahler’s compactness theorem, 357,
360, 362
map, 4
mapping, 4
Markov
spectrum, 210, 219
triple, 210–211, 222
marriage theorem, 78
Maschke’s theorem, 411, 431
Mathieu groups, 251, 254, 255
‘matrix’, 162, 168
matrix theory, texts, 79, 257
maximal ideal, 64, 148, 269, 274
maximal totally isotropic subspaces, 296
Mazur’s theorem, 570
mean motion, 458, 489
measurable function, 29, 466
measure theory, texts, 489
measure zero, 29, 32, 482
measure-preserving transformation,
466–473, 477–484
meet, 2
Mellin transform, 573
M ́eray–Cantor construction of reals, 18,
26
Merkur’ev’s theorem, 324
meromorphic function, 48, 263, 512,
538
Mersenne prime, 158–159, 175
Mertens’ theorem, 364
method of successive approximations,
32, 36, 38
metric space, 27–32, 72, 255, 268
Meyer’s theorem, 313, 316
minimal
basis, 173
model, 571, 580, 583
polynomial, 283
vector, 345, 346
minimum of a lattice, 345–347, 356,
357
Minkowski’s theorem on
discriminant, 330, 358
lattice points, 328–330, 338–339, 358
linear forms, 328
successive minima, 339–341, 358
minor, 171
mixing transformation, 480, 483
M ̈obius
function, 156, 390–392, 395
inversion formula, 156–157, 175
modular
elliptic curve, 573–574, 578, 584,
586
form, 258, 544, 573–574, 578, 583