Number Theory: An Introduction to Mathematics

608 Index

element, 90
integer, 90, 140
polynomial, 103, 112
square-norm, 342, 345
star discrepancy, 459, 464
Steiner system, 250
step-function, 449
Stieltjes integral, 220, 368, 394
Stirling’s formula, 328, 380
Stone’s representation theorem, 62, 76
Stone–Weierstrass theorem, 488
strictly proper part, 211
strong
Hasse principle, 317–318
triangle inequality, 30, 32, 262
structure theorem
for abelian groups, 172, 569
for modules, 172
subadditive ergodic theorem, 489
subgroup, 56–57
subset,2,61
subspace, 65–68
successive
approximations, 32, 36, 38
minima, 339–341, 358
successor, 5
sum of
linear maps, 68
modules, 166–167
natural numbers, 6–7
points of elliptic curve, 556, 583
representations, 411, 412
subspaces, 65
sum of squares, 51, 55, 78, 126, 544,
581
four, 51, 120–122, 218, 541–542
three, 108, 120, 318–319
two, 108, 119–120, 199–201, 218,
247, 542–544
for polynomials, 322–323, 325
for rational function, 323–324, 325
supplements to law of quadratic reci-
procity, 133, 314
supremum, 19, 22
surface
area of ellipsoid, 495–496

of negative curvature, 388–389, 395,

482, 483

surjection, 4

surjective map, 4, 10, 68

Sylvester’s law of inertia, 297

symmetric

difference, 61, 465

group, 57, 227, 423–425

matrix, 232, 238–239, 292–294, 301

relation, 4

Riemannian space, 219

set, 328, 341

symmetric 2-design, 249

symmetry group, 346, 430

symmetry operation, 430

symplectic matrix, 219, 440, 442

systems of distinct representatives, 78

Szemeredi’s theorem, 484–485, 490

tangent

space, 440, 481–482

to affine curve, 550

to projective curve, 550

taxicab number, 117

Taylor series, 48, 373, 406

t-design, 250, 254–255

tensor product, 68, 303

theta functions, 379, 519–525, 530, 535,

541–544

of lattice, 538

tiling, 204,337, 343, 344, 346, 358,

359, 499

topological

entropy, 388

field, 268

group, 432, 440, 442, 443

topology, 28, 268

torsion

group of elliptic curve, 569–570, 577

subgroup, 59, 172

submodule, 172

torsion-free, 346, 358

torus,n-dimensional, 439, 441, 472–473

total

order, 8, 18, 24

variation, 461–462, 489

totally isotropic subspace, 295–296, 299