Number Theory: An Introduction to Mathematics

Index 597

elliptic
curves, 555–558, 569–574, 582–583
functions, 509–516, 525–530
elliptic integral, 496–503, 536–537
of first kind, 498, 505, 514–516, 537
of second kind, 498, 505, 516–517,
530, 537
of third kind, 498, 506, 517, 530,
537
empty set, 2, 61
endomorphism of torus, 473, 483
energy surface, 465, 481
entropy, 482–483
equal, 2
equivalence class, 4
equivalence of
absolute values, 266
complex numbers, 184, 191, 201, 210
fundamental sequences, 26, 31
Hadamard matrices, 252
ideals, 151
matrices, 171
quadratic forms, 293, 297–298, 311,
317, 325
representation, 410, 416
equivalence relation, 4, 11, 26, 58, 106,
184
Erd ̋os–Turan inequality, 462, 489
ergodic, 465
hypothesis, 464–465, 470
measure-preserving transformation,
470, 472–473, 478–479
theorems, 466, 489
ergodic theory, texts, 489
error-correcting code, 28, 256, 258
Euclidean
algorithm, 91–92, 98, 104, 109, 121,
181, 560
distance, 28, 72, 346
domain, 104–106, 119–120, 124, 142,
171
metric, 342
norm, 229, 234, 342
prime number theorem, 134, 363
Euler’s
angles, 439

conjecture, 580–581, 584

constant, 159, 380

criterion for quadratic residues, 112,

135, 136, 159

formulas for coszand sinz, 45, 77

parametrization of rotations, 51–53

pentagonal number theorem, 545, 581

phi-function, 109–110, 114, 154–157,

389, 399, 403

prime number theorem, 363–364

product formula, 371, 381, 405

theorem on homogeneous functions,

551

even

lattice, 349, 351

permutation, 57, 130, 224, 227

eventually periodic, 18, 277

continued fraction, 192

exceptional simple Lie algebra, 442,

444

existence theorem for ordinary differ-

ential equations, 36–38, 76, 510

exponential

function, 38–39, 45–47

series, 38, 45

sums, 388, 489

extended Riemann hypothesis, 385,

395, 409

extension of absolute value, 273,

283–284, 290

extension of field, 45, 67, 283–284,

288, 386

exterior algebra, 256

extreme point, 236

face, 343

facet, 343–345

vector, 344–346

factor, 83, 146

group, 58–59

factorial domain, 90, 101, 124, 151,

153, 175

factorization, 124, 127

Faltings’ theorem, 215, 575, 583

Fano plane, 248, 250

Fermat equation, 142, 151, 575, 576,

579