596 Index
polynomial, 96–97
representation, 410, 414
De Morgan’s laws, 3
dense, 17–18, 275, 447
sequence, 448, 452
subset of metric space, 31, 270
densest
lattice, 348, 350–351, 359, 362
packing, 359–360
density of lattice packing, 348
derivative, 33–36, 67, 103
designs, 247–251, 254–258
determinant, 53, 180, 181, 224–229,
256
of lattice, 333, 347, 356
of quadratic space, 293
diagonal matrix, 225
diagonalization of quadratic form, 237–
239, 294, 297
difference of sets, 3
differentiable map, 33–34, 43, 75
differential form, 256
dimension of vector space, 67
Diophantine
approximation, 185, 212, 217, 219,
329, 358
equation, 161, 178, 195–201, 215–
217, 219
direct product of groups, 53, 60, 117,
172, 401, 429, 443
direct sum of
rings, 64, 117
vector spaces, 65
Dirichlet
L-function, 404–409, 443
character, 403–404, 574
domain, 342
product, 152–156, 175, 389
series, 175, 389,572
Dirichlet’s
class number formula, 218
convergence criterion, 138
Dirichlet’s theorem on
Diophantine approximation, 329
primes in arithmetic progression, 218,
313, 316, 400, 443
units in number fields, 176
discrepancy, 459–464, 488
discrete
absolute value, 275, 276
group, 203, 330
set, 342
subgroup, 330, 490
discriminant of
binary quadratic form, 205–207
elliptic curve, 553, 570, 579, 580
lattice, 333
quadratic irrational, 191
disjoint sets, 2
distance, 18, 27–31
distributive
lattice, 85
law, 7, 60, 85
divisibility tests, 107
divisible, 83, 87, 146
division
algebra, 54, 78
algorithm, 14, 90, 98
ring, 62–70, 125
divisor, 83, 386
of zero, 14, 62
doubly-periodic function, 514–517,
527, 538
dual
2-design, 249
convex body, 340
group, 401, 434, 443
lattice, 334, 340, 538
duality theorem, 435
dynamical system, 30, 388, 395, 447
Dynkin diagrams, 359e, 38, 187
echelon form, 164
eigenvalue, 239, 257, 430
eigenvector, 239
Eisenstein
integers, 141–143
irreducibility criterion, 102, 124
element, 2
elementary group, 425
ellipse, 237, 493–494
ellipsoid, surface area of, 495–496