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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
Q-additive function      389
q-additive functions      388
q-analog of log-concavity      513
q-analogs of Euler numbers      559
q-analogue of a positive integer      481
q-analogue of Bell numbers      486
q-analogue of Jordan’s totient      286
q-analogue of power series      486
q-analogue of the classical Euler totient      286
q-analogue of the classical Ramanujan sum      286
q-analogue of the p-adic measure      566
q-ascending factorial      569
q-Bernoulli numbers      483 561
q-Bernoulli polynomials      562
q-binomial coefficient      471
q-binomial coefficients      480 506
q-Euler numbers      561
q-Eulerian numbers      569
q-Eulerian polynomials      570
q-exponential polynomial      483
q-generated number      384
q-Hurwitz $\zeta$-function      565
q-log-$\Gamma$ function      563
q-multinomial coefficients      506
Q-multiplicative      406
q-Niven number      382
q-Riemann $\zeta$-function      562
q-Stirling numbers      481 504
q-tangent numbers      559
q-trigonometric function      561
Quadratic character      554
Quadratic field      285 293
Quadratic fields      32 252
Quadratic residue      216
Quadri-amicable numbers      70
Quasi-amicable pairs      68
Quasi-multiplicative functions      270
Quasi-multiplicativity      116
Quasi-orthogonality      476
Quasi-superperfect      41
Quasiperfect numbers      36
Queues      464
r-Stirling numbers      469
Ramanujan expansions      278
Ramanujan identities      536
Ramanujan sum      184 258 277
Ramanujan sums      125 137
Ramanujan sums on semigroups      277
Ramanujan theorems      544
Ramanujan’s sum      265
Ray method      516
Reciprocal GCD and LCM matrices      272
Recursive algorithm      223
Recursive set      32
Redei’s generalization of Euler’s theorem      208
Refined Stirling numbers      487
Regular arithmetic convolution      144
Regular convolution      112
Regular convolutions      183
Regular polygon      188 239
Regular S-representation      285
Relatively k-prime      136 275
Relatively prime amicable pairs      65 66
Relatively prime amicable pairs of opposite parity      66
Remarkable identities      282
Representations of real numbers      432
Repunit number      383
Residue classes      387
Residue classes modulo n      249
Residue theorem      478
Resolution function      367
Resultant of cyclotomic polynomials      262
Reversing the digits      429
Riemann hypothese      262
Riemann hypothesis      102 129 130
Riemann zeta function      99 187 263 330 510 527
Riesz representation theorem      185
Right inversion      123
Right inversion formula of Mobius type      123
Rising factorial power      461
Roots of unity      184 393
Roth’s theorem      426
Rudin — Schapiro sequence      396
S-perfect numbers      55
Saddle point method      516 583
Salem numbers      415
Schemmel totient      184
Schemmel totient function      229
Schemmel — Nagell totient      133 276
Schemmel’s totient      133 216 276
Schinzel — Szekeres function      356
Schinzel’s conjecture      218
Schinzel’s H-Hypothesis      380
Schinzel’s Hypothesis H      198 221
Schmidt’s subspace theorem      418 508
Schrodinger operators      391
Schur’s Theorem      260
Secant numbers      559
Second order Eulerian numbers      580
Selberg’s identity      160
Selberg’s upper bound sieve      226
Self-number      384
Semi-multiplicativity      116
Semi-unitary divisor      281
Semi-unitary greatest common divisor      271
Semi-unitary product      128
Semigroup approach to the Fermat and Euler’s theorems      191
Semigroups with unique factorization      150
Semisimple rings      333
Sequence ($B_k$ (mod«))      555
Sequence of Eulerian numbers      577
Sequences of Fibonacci, Pell, and Lucas      59
Set of totients      206
Shapiro — Pillai function      200
Shintani zeta functions      536
Siegel — Walfisz theorem      248
Sieve of Eratosthenes      338
Sieve theory      103
Sieve-theoretical problems      355
Sigmoid function      569
Signed Eulerian polynomial      570
Signless Bernoulli numbers      525
Signless q-Stirling numbers of the first kind      481
Silverman constant      182
Simple groups      157
Simple pole      415
Sita Ramaiah’s Mobius function      113
Small prime divisors      341
Small sieve      359
Smallest prime totative      248
Smarandache function      22 210 237
Smith brothers      384
Smith number      383
Smith — Jones number      384
Sociable number of order k      75
Sociable numbers      72
Soluble group      155 157
Soluble groups      154
Special cyclotomic polynomials      252
Spectral norm of a matrix      274
Square-reduced residue system      289
Square-totient of R. Sivaramakrishnan      289
Squarefree integers      33 207 265
Squarefree number      35 46
Squarefree numbers      136
Squarefull      209
Squarefull integers      331
Staggered sums      429
Statistic on permutations      479
Statistical convergence      331
Statistical limit      335
Stevens totient      280
Stevens’ totient      280
Stieltjes transforms      525
Stirling functions of the first kind      473
Stirling functions of the second kind      473
Stirling numbers associated to a matrix      475
Stirling numbers of complex argument      487
Stirling numbers of complex arguments      523
Stirling numbers of fractional order      472
Stirling numbers of the first kind      462 479
Stirling numbers of the first kind $s_t(n, k)$ associated to the sequence t      41A
Stirling numbers of the second kind      460 578
Stirling numbers of the third kind      464
Stirling polynomials      466 469
Strassen functional      343
Strong log-concavity      508
Strong regular A -convolution      119
Strongly q-additive      411
Strongly q-log-concave      514
Subadditive functions      344
Subblock occurrences      422
Subgroup      151 157
Sublime numbers      22
SubMatrix      269
Subring      142
subspace      185
Sugcd-closed      271
Sum of digits      371 499 551
Sum of digits of primes      379
Sum of digits with prime indices      390
Sum of divisors      180 264
Sum of jth powers of totatives      242
Sum of prime digits      390
Sum of totatives      242
Sum-product numbers      383
Super-lovely pair      69
Super-multiplicative      355
Supermultiplicative      346
Superperfect number      58
Superperfect numbers      23 38 69
Suzanne sets      384
Sylow p-subgroup      155
Sylow subgroups      158
Symmetric signed digit expansion      422
Symmetric system      422
Symmetries and dualities      476
T-chain      370
Tangent numbers      527 559 577
Taylor expansion      488
te Riele’s trick      63
Teichmuller character      554
Thabit’s rule      17 61
Thacker’s function      243
Thacker’s totient function      289
The characteristic      511
The exponential A -convolution      118
Theorem by J. Touchard      29
Theorem by Touchard      35
Theorem of Adams      541
Theorem of Howard      551
Theorem of Sylvester      25
Theorem of Sylvester and Lipschitz      548
Theoretical physics      375
Theory of Mobius function      139
Thue-Morse sequence      379
Thue-Morse sequences      390
Total number of prime divisors      180
Total number of prime factors      26 133 137
Totatives      179 242
Totient functions      125
Totient-free residue classes      206
Touchard’s congruence      495
Trace languages      161
Trace monoids      161
Transcendence      391
Transcendental      426
Transitive orientation      162
Triangular matrices      265
Triperfect numbers      34
Twin dragon      421
Twin primes      234
Twin-prime constant      219
ud-closed      271
Ultrametric Banach space      546
Unambiguous lifting      162
Unambiguous Mobius function      162
Unequal characters      554
Uniform asymptotic      524
Uniform asymptotic expansion      518
Uniform limit distribution mod m      389
Uniform probability measure      343
Uniform summability      413
Uniformly distributed mod 1      410
Uniformly distributed mod m      389
Uniformly distributed modulo 1      397
Uniformly periodic      427
Unimodal      577
Unique factorization domains      32
Unitary abundant numbers      46
Unitary aliquot sequences      74
Unitary almost perfect numbers      47
Unitary almost superperfect number      47
Unitary almost-sociable numbers      75
Unitary amicable numbers      67
Unitary analogue of Euler’s totient      242
Unitary analogue of Legendre’s totient      284
Unitary analogue of Nagell’s totient      281
Unitary analogue of Ramanujan’s sum      267
Unitary analogue of Schemmel’s totient      281
Unitary analogue of Smith’s determinant      266
Unitary analogue of the Carmichael’s conjecture      229
Unitary analogues of generalized Ramanujan sums      277
Unitary convolution      112 127
Unitary divisor      46
Unitary harmonic numbers      49 50
Unitary hyperperfect numbers      51
Unitary m-perfect numbers      57
Unitary Mobius function      111 272
Unitary multiply superperfect numbers      48
Unitary perfect numbers      45
Unitary product      110
Unitary product set      111
Unitary quasi superperfect numbers      47
Unitary quasi-sociable numbers      75
Unitary quasiperfect numbers      47
Unitary Smith determinants      271
Unitary sociable numbers      74
Unitary superperfect numbers      47
Unitary totient function      213 266
Universal Bernoulli numbers      552
Universal generated      385
Unsigned Lah numbers      464
Unsigned Stirling numbers of the first kind      462
Unsolved problems on generalized integers      125
Upper density      345
Valence function of $\varphi$      226
Vector space      145 286 420 481
von Mangoldt function      160 259
von Staudt — Clausen and Voronoi type congruences      554
von Staudt — Clausen theorem      245 539
von Sterneck and the Cohen totients      275
Waring’s problem      421
Weak convergence of distribution functions      343
Weakly-composite      340
Weird numbers      43 44
Well-distributed mod 1      411
Weyl derivative      474
Weyl’s lemma      421
Wieferich prime      212
1 2 3 4 5
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