Number Theory: An Introduction to Mathematics

Index 605

part, 211
ring, 87, 104
polytope, 343, 358
Pontryagin–van Kampen theorem, 435
positive
index, 297
integer, 13–14
measure, 433
rational number, 16–17
real number, 18, 22
semi-definite matrix, 235, 239
positive definite
matrix, 235, 239
quadratic form, 205
quadratic space, 296
rational function, 323–324
power series, 45, 46, 48
primality testing, 124, 127
prime
divisor, 386
element, 89, 145
ideal, 148–151, 384–385
ideal theorem, 385, 393, 395
number, 88–89
prime number theorem, 365–367, 369–
377, 390, 394–395
for arithmetic progressions, 394, 400,
403–408
primitive
Dirichlet character, 409
polynomial, 100
quadratic form, 206
root, 115–116, 124–125, 385
root of unity, 111, 112, 114
principal axes transformation, 238, 257
principal character, 401
principal ideal, 91, 145
domain, 92, 95–96, 98, 104,
105–106, 168–172
principle of the argument, 533
probability
measure, 466
space, 466
theory, 29, 75, 76, 391, 395, 582
problem of moments, 220
problem, 3x+1, 490

product

formula for theta functions, 519, 521

formula for valuations, 267

measure, 476

of ideals, 145

of integers, 12

of linear maps, 67

of natural numbers, 7

of rational numbers, 16

of representations, 411

of sets, 3

projective

completion, 550–551, 552–553

conic, 550

cubic, 550

equivalence, 551–553

line, 550

plane, 248, 250, 321, 325

plane curve, 550

space, 53

proper

divisor, 89

subset, 2

properly equivalent

complex numbers, 184, 201

quadratic forms, 205–206

properly isomorphic, 347

public-key cryptography, 124

Puiseux expansion, 44

pure

imaginary complex number, 41

quaternion, 51, 52

Pythagoras’ theorem (or law), 17,

73–74, 108

Pythagorean triple, 108, 217

q-binomial coefficient, 95, 581

q-difference equation, 546

q-hypergeometric series, 581

q-integral, 581

quadratic

field, 105–106, 124, 140–151, 174,

207, 218

form, 205–207, 291–293, 563

irrational, 191–194, 206, 209–210,

214, 537

nature, 129, 133