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Sandor J., Mitrinovic D.S., Crstici B. — Handbook of Number Theory II
Sandor J., Mitrinovic D.S., Crstici B. — Handbook of Number Theory II

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Название: Handbook of Number Theory II

Авторы: Sandor J., Mitrinovic D.S., Crstici B.

Аннотация:

This handbook focuses on some important topics from Number Theory and Discrete Mathematics. These include the sum of divisors function with the many old and new issues on Perfect numbers; Euler's totient and its many facets; the Möbius function along with its generalizations, extensions, and applications; the arithmetic functions related to the divisors or the digits of a number; the Stirling, Bell, Bernoulli, Euler and Eulerian numbers, with connections to various fields of pure or applied mathematics. Each chapter is a survey and can be viewed as an encyclopedia of the considered field, underlining the interconnections of Number Theory with Combinatorics, Numerical mathematics, Algebra, or Probability Theory. This reference work will be useful to specialists in number theory and discrete mathematics as well as mathematicians or scientists who need access to some of these results in other fields of research.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 637

Добавлена в каталог: 12.09.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$(\alpha, \beta)$-multiamicable numbers      71
$A_k$-convolutions      113
$l_p$ norm $(p \geq 1)$ of matrices      274
$\alpha$-adic representation      419
$\gamma$-perfect numbers      54
$\mathcal{R}$-multiplicative      407
$\mathcal{R}$-system      407
$\mathcal{U}$-Stirling numbers      485
$\psi$-multiperfect numbers      41
$\psi$-superperfect numbers      40
$\psi\circ\sigma$ -perfect numbers      4
$\sigma\circ\psi$-perfect numbers      40
$\varphi$-amicable pairs      71
$\varphi$-convergence      187
$\varphi$-partitions      223
(A, r)-powerful      114
(m, k)-perfect      41 42
1-c product      126
3x + 1 problem      190
A-analogue of Smith’s determinant      266
A-convolution      112 278
A-multiplicative      114
A-rational function      114
Abelian minimal normal subgroup      155
Abelian number fields      553
Abstract prime number theorems      154
Abundant numbers      17 43
Action of the cyclic group      490
Adding composite totatives      248
Adding prime totatives      248
Additive analogue of Euler’s totient      291
Additive analogue of the a      292
Additive arithmetic function      366
Adjacent slices      568
Airy asymptotic      524
Algebraic function fields      161
Algebraic independence of real valued arithmetic functions      185
Algebraic integers      293 421
Algebraic number field      159 263 419
Algebraic number fields      193
Algebraic number theory      160
Algebraic numbers      553
Algebraic topologies      499
Algebraic topology      162
Algorithms      36 419
Aliquot sequence      72 74
All-Niven      383
Alladi’s totient      282
Almost all sums      340 342
Almost amicable pairs      69
Almost perfect numbers      37 38
Almost superperfect numbers      41
Amicable k-tuples      70
Amicable numbers      36 60 63
Amicable numbers in special sequences      67
Amicable triples      69
Analogue of Adams’ theorem      557
Analogue of Euler’s formula      62
Analogue of Lehmer’s problem      213 214
Analogue of Smith’s determinant      266
Analogue of Thabit’s formula      62
Analytic continuation      582
And Mellin — Perron summation formula      423
Aperiodic elements      490
Apostol function      129
Applet, which computes the values $\varphi(n)$ and $\lambda(n)$      193
Applications of Mobius inversion formulae      156
Applications of the Mobius functions      139
Approximation theory      469
Arithmetic process      343
Arithmetic progression      221
Arithmetic progressions      136 151 220 229 254
Arithmetical products      285
Arithmetical semigroup      149
Arithmetical semigroups      292 331
Arithmetical triangles      502
Ascents      567
Associated Stirling numbers      502 580
Asymptotic analysis      511
Asymptotic behavior of the Stirling numbers      516
Asymptotic density      363
Asymptotic development of the Stirling numbers of the first kind      515
Asymptotic expansions of Stirling numbers of the second kind      520
Asymptotic normality      416
Asymptotic normality of Eulerian numbers      579
Asymptotic prime divisor      341
Asymptotic sign fluctuations      517
Asymptotically Poisson distributed      518
Asymptotically unit exponential variables      341
Automorphic numbers      431
Average number of blocks      512
b-additive      404
B-convolution      116
B-splines      471
Baker’s method      418 430
Barrucand numbers      494
Base q palindromes      430
Basis      481
Bassily — Katai theorem      403
Bauer’s theorems      245
BDE method      61 63
Bell number      461
Bell numbers      493
Bell polynomials      484 495
Bell sequence      512
Benford law      430
Bernoulli and Euler polynomials      529 582
Bernoulli and Stirling numbers      259 467
Bernoulli number      461
Bernoulli numbers      243 244 495 500 518 525
Bernoulli numbers of fractional order      474
Bernoulli numbers of higher order      500
Bernoulli numbers of order k      468
Beta-expansions      432
Betrothed numbers      68
Beurling’s generalized primes      207
Bi-unitary amicable numbers      67
Bi-unitary convolution      111
Bi-unitary divisor      46
Bi-unitary multiply perfect numbers      47
Bi-unitary perfect numbers      47
Bi-unitary quasiperfect      47
Bilinearly recurrent orthogonality      476
Binary recurrence sequence      240
Binomial coefficient      49 107 126 371
Binomial coefficients      243 460 474
Binomial convolution of sequences      117
Binomial measure      375
Biological analogies      17
Bipartite graphs      348
Birational transformation      192
Block-additive      410
Block-multiplicative      408
Bohr almost-periodic function      136
Bohr — Fourier spectrum      413
Bolyai — Renyi expansions      432
Bombieri’s sieve      227
Boole summation formula      577
Boolean lattice      513
Borel $\sigma$-algebra      344
Bounded below set      148
Bounded variation      103
Brauer — Rademacher identity      144 180
Britannic number system      407
Brownian motion      344
Brun — Titchmarsh theorem      216 227
Brun’s Sieve      235
Buchstab function      357
Burnside Basis Theorem      293
C++ programming language      217
Cancellation property      120
Canonical basis      393
Canonical number system      418
Canonical number systems      404
Cantor representations      412
Carlitz congruence      552
Carmichael conjecture      228
Carmichael’s theorem      190
Carmichael’s X function      193
Cashwell — Everett totient      280
Catalan’s conjecture      73
Cauchy product      117 122 128
Cauchy’s integral formula      579
Central factorial numbers      479
Central limit theorem      344 402 423
Chain      72 369
Chains      141 144
Change of the sum of digits by multiplication      378
Character group      151
Characteristic equation      240
Characteristic polynomial      414
Characters of finite abelian groups      151
Chebysheff’s theorem      207
Circle of convergence      415
Circulant matrix      183
Circular permutations      192
Classical Mobius function      99 128 135
Code      179 396
Coefficients of cyclotomic polynomials      256
Cohen totient $\varphi_S$      290
Combinatorial and statistical applications      480
Combinatorial applications      107 477
Combinatorics on words      390
Common generalization of Liouville’s function and the Mobius function      137
Commutative group      106
Commutative ring      110 121
Commutative semigroup      117 118
Commutator subgroup      158
Complete asymptotic expansion      520
Complete symmetric functions      471
Complex bases      417
Complex variables      381
Composition of $\varphi$ and other functions      234
Composition of some arithmetic functions      39
Computational evidence      42
Computer algebra      486
Conductor      553
Congruence of Kummer      541
Congruence of Voronoi      541
Congruence properties      477
Congruence properties of $\sigma^{(m)}(n)$      42
Congruence properties of Euler’s totient      201
Congruence property      188
Congruences for Genocchi numbers      541
Congruences for higher order Bernoulli numbers      549
Congruences for Stirling numbers      488
Conjecture      42 47 51—53 59 195 229 235 241 348 382 400 494 499 556 558 573
Conjecture of Sierpinski      229
Conjectured      46 352
Conjectures      199 216 237 557
Conjugacy classes      157
Conjugate Bernoulli numbers      538
Conjugate Bernoulli polynomials      538
Consecutive divisors      342
Consecutive prime factors      337
Constants      181
Continued fractions      432 537 561
Continued powers and roots      432
Convex polytope      559
Convolution of incidence functions      139
Convolution on the set of sequences      537
Convolutions with unbounded unity      128
Core      208
Core-reduced residue system      290
Core-reduced totient of J. Sandor and R. Sivaramakrishnan      290
cosets      151
Counterexample to Carmichaers conjecture      228
Criptography      15
Cross-convolution      113
Cumulative distribution function      397
CYCLE      72 427
Cycles      73 75 183 462 479 491
Cyclic homology      570
Cyclotomic Bernoulli numbers      539
Cyclotomic field      539
Cyclotomic fields      556
Cyclotomic polynomial      27 138 139 203 251 256 506 571
Cyclotomic polynomials      24 261
Daykin’s Mobius inversion formula      110
Dedekind arithmetic function      39
Dedekind arithmetical function      231 284
Dedekind domains      191
Dedekind zeta-function      293
Deficient numbers      17 43
Degenerate Eulerian numbers      572
Degenerate weighted Stirling numbers      476
Degree of resolution      367
Dense      331
density      221
Density of amicable pairs      65
Density of e-perfect numbers      52
Density of friendly pairs      70
Density of harmonic numbers      44
Density of k-perfect numbers      33
Density of multiamicable numbers      71
Density of odd perfect numbers      30
Derangements and cycle indicators      507
Derived k-cycle      337
Derived sequence      337
Descents      570
Determinant      269
Determinants      265
Determinants involving q-Stirling numbers      483
Dibag’s von Staudt — Clausen theorem      553
Dickman function      359
Dickson — Eulerian numbers      571
Dickson — Stirling numbers      477
Dickson’s Conjecture      221
Dickson’s theorem      30
Difference operator      123
Differential equation      567
Differential equations      469
Differential geometry      390
Digits of Fibonacci numbers      430
Diophantine approximations      263
Diophantine equation      28 61
Diophantine equations      107
Direct factor set      135
Directed graph      183
Dirichlet convolution      112 117 127
Dirichlet density      152
Dirichlet inverse      120
Dirichlet inversion      123
Dirichlet product      106 109 119 132
Dirichlet series      100 131 243 423
Dirichlet set      206
Dirichlet’s theorem on arithmetical progressions      210
Discrete analog of integration by parts      145
Discriminator      211
Distance geometry      486
Distinct divisors      347
Distribution (mod 1) on divisors      366
Distribution function      242 345 351 353 402 524
Distribution functions      355
Distribution in residue classes      206
Distribution of Bernoulli numbers modulo primes      556
Distribution of primes      211
Distribution of totatives      246
Divided differences      469
Divisibility algorithm      191
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