Number Theory: An Introduction to Mathematics

Index 609

totient function, 110
trace of
matrix, 414
quaternion, 49–50
transcendental element, 386
transcendental number, 174, 578, 583
transformation formulas
for elliptic functions, 512, 528–529,
538
for theta functions, 377–379, 520,
522
transitive
law, 8
relation, 4
translation, 346
of torus, 472, 483
transpose of a matrix, 227, 229
triangle inequality, 27, 262
triangular matrix, 229
trichotomy law, 8
trigonometric
functions, 45–47, 77
polynomial, 450, 488
trivial
absolute value, 262, 273
character, 401
representation, 410
ring, 62
TW-conjecture, 574, 578, 580, 584, 586
twin prime, 392–393, 395
twistedL-functions, 574
2-design, 247–250, 258
type (A) Hilbert field, 308–310
type (B) Hilbert field, 308–311

ultrametric inequality, 262, 273, 277
uniform distribution, texts, 488
uniformization theorem, 218
uniformly distributed mod 1, 448–458
union of sets, 2–3, 61
unique factorization domain, 90
unit, 62, 87, 108, 144–145, 153
unit circle, 47–48
unit tangent bundle, 481–482
unitary
group, 440, 442
matrix, 53, 437

representation, 412, 434, 437

symplectic group, 440, 442

universal quadratic form, 295, 297

upper

bound, 19, 22

density, 484

half-plane, 201, 208–209, 519, 531,

534

limit, 24

triangular matrix, 229

valuation

ideal, 274–276

ring, 88, 274–276

valuation theory, texts, 290

value, 4

group, 262–263, 274, 276

valued field, 261–264

van der Corput’s

difference theorem, 454, 458

sequence, 463, 464

van der Waerden’s theorem, 485–488,

490

vector, 64

space, 64–70

vertex of polytope, 343

volume, 327

von Mangoldt function, 370, 372

Voronoi cell, 342–346, 349, 359

of lattice, 344–346, 353–357, 359

Voronoi diagram, 358

Waring’s problem, 122–123, 126

weak Hasse principle, 317

Wedderburn’s theorem on

finite division rings, 125

simple algebras, 69

Weierstrass approximation theorem, 74,

450, 488

weighing, 233–236, 257

matrix, 234–236, 257

weight of vector, 254–256

Weil conjectures, 387–388, 395

Weyl’s criterion, 451

Wiener’s Tauberian theorem, 367, 394

Wiles’ theorem, 575, 580, 584

Williamson type, 233