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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
K-convolution      114 115
k-Eulerian posets      148
k-free part      134
k-full      236
k-fullpart      134
k-harmonic number      44
k-hyperperfect numbers      50
K-iterate of an arithmetical function      115
k-Mobius function of a poset      147
k-multiperfect numbers      30
k-perfect number      32
k-perfect numbers      33
k-reduced residue system      276
k-Smith number      383
k-th power of an arithmetic function      108
k-unitary perfect number      46
Kanold’s method      30
Kaprekar numbers      22
Kaprekar routine      429
Kesava Menon’s totient      281
Klee’s method      228
Klee’s Mobius function      278
Kloosterman-sums      250
kth cyclotomic polynomial      561
kth iterate of f      196
Kubilius class      344
Kummer type congruences      552 554 567
Kurepa’s left-factorial function      495
l.c.m.-product      119
Lagrange theorem      245
Lagrange’s Theorem      488
Lah numbers      578
Lah’s numbers      478
Laplace integrals      583
Laplace method      579
Laplace’s rule      259
Large prime divisors      341
Lattice      141
Lattices of subgroups of a group      139
Law of iterated logarithms      364
lcm-closed sets S      271
Least common multiple      348
Least nonnegative residue      543
Least prime divisor      355
Left inversion      123
Left-factorial function      573
Legendre formula      371
Legendre symbol      250 396 547
Legendre totient      283 287
Legendre totient of u arguments      285
Legendre — Jacobi symbol      183
Legendre — Stirling numbers      488
Lehmer $\psi$-product      128
Lehmer, McCarthy, and Erdos theorems      247
Lehmer’s conjecture      212
Lehmer’s totient function      289
Leudesdorf’s theorem      244
Limit distribution mod m      389
Limiting distribution      540
Linear forms in logarithms      508
Linear groups      186
Linear independence over $\mathbb{Q}$      263
Linear recurrences      414
Linear transformations      185
Liouville function      116 137
Local limit law      416
Locally distributive      143
Locally finit poset      142
Log-concave function      524
Log-concavity      577
Logarithm operator      108
Logarithmic and identric means      486
Logarithmic convexity      471
Logarithmic distribution function      397
Logarithmic Fourier series      398
Logarithmic polynomials and numbers      533
Logarithmically concave      470
Lovely numbers      69
Lower closed sets      267
Lower density      236
Lubin — Tate groups      566
Lucas sequence of the first kind      240
Lucas sequence of the second kind      240
Lucas sequences      36
Lucas’ totient      277
m -unitary (k, l)-perfect number      57
m — e-perfect numbers      58
m — e-superperfect numbers      58
m-bi-unitary perfect numbers      57
m-bi-unitary superperfect numbers      58
m-integral      539
m-multisuperperfect numbers      55
m-perfect numbers      55
m-superperfect numbers      39 56
M-void analogue of the Euler totient      290
Mac Mahon’s Master theorem      161
Magic squares      184
Magma system for computational algebra      258
Maillet’s theorem      207
Makowski — Schinzel conjecture      235
Marriage theorem      348
Matched asymptotic expansions      516
Matrix-generated convolutions      127
Maximal generalization of Fermat’s theorem      190
Maximum and minimum exponents      330
Maximum of the exponents      355
Mean value      401
Meet semilattice      267
Meet-closed sets      273
Meet-closed subset      268
Meet-matrix      268
Mellin transform      566
Mersenne prime      21 22 234
Mersenne primes      15 19 41 42 222
Metabelian group      159
Methods of Voronoi      545
Miller — Rabin and Lucas tests      218
Minimal polynomial      420
Minimal, normal, and average order of Carmichaers function X      193
Minkowski product      104
Mobius categories      148
Mobius function      153 154 264 268 490 496
Mobius function $\mu_G$      128
Mobius function associated with the dual poset      157
Mobius function generated by the B-convolution      116
Mobius function of a direct product      158
Mobius function of a generalized integer      125
Mobius function of a set of primes      105
Mobius function of a trace monoid      162
Mobius function of geometric lattices      148
Mobius function of n arguments      109
Mobius function of P      140
Mobius function on a subset of a power set      154
Mobius functions of arbitrary direct factor sets      135
Mobius inversion      102—104 148 490
Mobius inversion formula      180 251
Mobius inversions      482
Mobius system      104
Mobius type inversion theorems      150
Mobius-type function      193
Mobius-type inversion formula      135
Mobius-type inversion formulae      125
Mobius’ function      184
Mobius’ function of an arithmetical semigroup      148
Modern computers      24
Modified q-Bernoulli numbers      564
Modified q-Bernoulli polynomials      564
Modified Stirling numbers      500
Modular group      272
Modular idempotent numbers      431
Monica sets      384
Monoids with finite decomposition property      148
Multidimensional Smith’s determinants      266
Multiperfect numbers      32 35
Multiplicative inverse of t      250
Multiplicative semigroup      105
Multiply perfect numbers      32 35 71
n -dimensional symplex      568
n-permutations with $\eta$-colored head      480
n-th prime $p_n$      180
Nagell’s totient      133 278
Narkiewicz Mobius function      144
Narkiewiecz Mobius function      113
Narumi polynomials      550
Negative integer bases      417
Newton’s formulae      258
Nielsen polynomials      467
Nilpotent elements      118 290
Niven number      381
No unitary m-superperfect numbers      57
Non-central Stirling numbers      479
Non-commuting lifting      162
Non-crossing set partitions, schuffie posets      148
Non-divisibility property      202
Noncototients      208
Nontotient      230
Nonunitary aliquot sequences      76
Nonunitary amicable pairs      68
Nonunitary divisors      48
Nonunitary k-cycle      76
Nonunitary perfect numbers      48
Nonunitary totient function      287
Normal order      332
Nowhere differentiable      373 375 392 400 417
Nowhere differrentiable      399
nth prime      234
nth symmetric mean      471
Number of decimal digits      431
Number of digit blocks of 11      426
Number of distinct prime divisors      33 110 180
Number of distinct prime factors      28 243 250 265 283 519
Number of divisors      35 180 264
Number of odd digits      425
Number of solutions of the congruence      279
Number of square-free divisors      130
Number of terminating nines      426
Number of unitary divisors      284
Occurrences of the block w      425
Odd amicable pairs      64
Odd perfect number      25 28 29 31 33 34 41
Odd perfect numbers      19 23 26 31
Open problem      203 209 222 272 349 416
Open problems      31 43 76 203
Open question      67 209
Operatorial theory      469
Optimization theory      339
Orbit      490
Orbits      481
Order of a modulo n      189
Order of the group      202
Orthogonal projection      394
Orthogonality      476 477 485
Orthonormal basis      185
Oscillatory asymptotic      524
Other analogs of Lehmer’s problem      215
Overlap      390
p -group      155
p, q-log-concavity      515
p, q-Stirling numbers      484
p-adic analysis      541
p-adic expansion      498
p-adic gamma function      566
p-adic integers      550
p-adic integrals      566
p-adic L function      566
p-adic log-gamma functions      566
p-adic mean value theorem      546
p-adic method      494
p-local integers      553
p-Stirling numbers      472
Palindrome      391
Parallelotope      420
Parametric Mobius inversion      145
Parry’s $\alpha$-expansion      415
Partial ordering      141
Partial p, q-Stirling numbers      486
Partial product      128
Partially ordered sets      105
Partition lattice q-analogs      481
Partitions      461
Pascal’s triangle      379
Pell sequence      67
Perfect number      369
Perfect totient number      240
Periodic mapping      554
Periodic perfect numbers      17
Periods of the Stirling numbers      492
Phibonacci number      223
Pillai arithmetic function      182
Piltz divisor function      106 107
Pisot number      415
Plato’s Republic      17
Pointwise product      119
Poisson process      341
Poly-Bernoulli numbers      501
Polya frequency sequence      578
Polya — Vinogradov inequality      554
Polylogarithm function      552
Polynomial ring      552
Polynomial sequences      402
POSET      139
Poset-theoretic generalization of Smith’s theorem      268
Positive definite      273
Power series      100
Power-harmonic number      44
Powerful      52
Practical numbers      59 359
Preferential arrangements      496
Primality criterion      254 256
Primary pseudoperfect number      45
Prime factors of $\Phi_n(a, b)$      255
Prime factors of $\varphi{(j)}(n)$      198
Prime factors of the Euler numbers      556
Prime ideal      293
Prime ideal theorem      160 161
Prime k-tuple conjecture      218
Prime number theorem      149 150
Prime-counting function $\pi(n)$      180
Prime-power groups      139
Primitive character      553
Primitive divisors of Lucas sequences      216
Primitive element      420
Primitive root mod n      251
Primitive root of unity      258
Primitive roots      189
Primitive roots of unity      138 251
Primitive solutions      197 198
Primitive substitution      374
Probabilistic group theory      364
Product of all divisors      55
Product of all e-divisors      58
Product of digits      383
Product of divisors      202
Product set      104
Pseudoperfect numbers      43
Pseudoprime      30
q -Euler function      286
q -Euler polynomials      563
q — L -series      563
q-additive      387 401
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