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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
Divisor density      366
Divisorial graph      369
Divisors in residue classes      363
Divisors of factorials      354
Dobinski’s formula      461
Double series      101
Double-factorial      483
Dynamical system      367
e-multiperfect      52
e-perfect numbers      52
e-superperfect numbers      53
Egyptean fractions      16
Eigenspace      394
Eigenvalue      393 409
Eigenvectors      393
Eingenvalues      393
Eisenstein series      544
Elementary abelian      156
Elementary symmetric function      510
Epimorphisms      158
Equidistributed (mod 1)      366
Erdos — Kac theorem      388
Erdos — Turan — Koksma inequality      405
Erdos — Wintner theorem      401
Ergodic theory      412
Euclid — Euler theorem      21
Euclidean division      570
Euclidean norm of a matrix      274
Euclid’s “Elements”      16
Euler factor      23 30
Euler functions of finite groups      293
Euler gamma function      563
Euler l.c.m. sequence      211
Euler maximal function      210
Euler minimum function      210
Euler numbers      527
Euler quotients      538
Euler totient      40 496
Euler totient of matrices      278
Euler — Maclaurin summation formula      547
Eulerian functions      571
Eulerian numbers      567
Eulerian numbers of higher order      571
Eulerian polynomials      477 568
Eulerian posets      146
Euler’s divisibility theorem      188 538
Euler’s function      22
Euler’s gamma function      523
Euler’s methods      61
Euler’s theorem      24
Euler’s totient      67 71 106 134 137 179 184 497 544 555
Euler’s totient function      269 272
Even functions (mod n)      184
Even perfect number      19 21 22 32 54
Even perfect numbers      20 22 23 44 59
Even-odd amicable pair      65
Exponential analogue $\mu^{(e)}$ of the Mobius function      118
Exponential Bell polynomials      477
Exponential convolution      117
Exponential cycles      75
Exponential divisor      51
Exponential inverse      118
Exponential operator      108
Exponential sum of digit counting function      379
Exponential sums      261
Exponential totient function      119 288
Exponentially A -multiplicative functions      119
Exponentially multiplicative functions      118
Extended Nagell totient      132
Extension of Nagell’s (and Alder’s) totient      279
f-expansions      432
f-generated number      386
f-iterative sequence      427
f-self-number      386
Factor-closed set      267
Factorable function      143
Factorable functions      127
Factorial base      386
Factorial numbers      478
Factorial ring      106
Factorization methods of integers      256
Factorization of Bernoulli numerators      556
Falling factorial      478
Falling factorial power      460
Fermat number      223
Fermat numbers      254
Fermat prime      27 191 239 527
Fermat primes      225 236
Fermat quotient      548
Fermat quotients      530
Fermat’s divisibility theorem      179
Fermat’s Little Theorem      488
Fermat’s quotient      211
Fermat’s “little theorem”      15
Fermionic oscillators      487
Fibonacci and Lucas numbers      182 498
Fibonacci numbers      398
Fibonacci or Lucas sequences      239
Fibonacci sequence      22
Fibonacci, or Lucas numbers      204
Finite alphabet      161 374
Finite automata      390
Finite field      192 286
Finite group      154 490
Finite p-group      293
Finite permutation groups      193
Finite poset      154
Finite recurrences      414
Flag      481
Formal languages      161
Formal Laurent series      488
Formal power series      162 426
Fourier analysis      415
Fourier coefficients      184 544
Fourier expansions      531
Fourier transforms      103
Fractal dimension      367
Fractional parts of the Bernoulli numbers      540
Frattini chief factor      155
Free Abelian group      151
Frequency of a block      421
Friendly pair      70
Frobenius congruences      544
Frobenius’ classical theorem      156
Function $\lambda$      189
Function by Jacobsthal      247
Functional limit theorems      416
Fundamental domains      421
G-ary digital expansion      414
G-convolution      121
G-multiplicative functions      121
Galois field      481
Gauss norm      547
Gauss sum      566
Gaussian integer      263
Gaussian integers      32 404
Gaussian limit law      399
Gaussian prime      26 263
Gauss’ Theorem      193
GCD matrices associated with arithmetical functions      273
gcd-closed matrices      270
gcd-closed set      270
gcud-closed      271
Gegenbauer’s theorem      192
General theorem of log-convexity      511
Generalization of Euler’s theorem      191 192
Generalization of Euler’s totient      246
Generalization of finite differences      475
Generalization of Mobius’ function      115
Generalization of the Mobius function      137
Generalizations of Euler’s totient      291
Generalizations of Klee’s totient      278
Generalizations of Ramanujan’s sum      277
Generalizations of Ramanujan’s sum to matrices      278
Generalizations of the Mobius function      139
Generalized arithmetical functions      140
Generalized Bernoulli numbers      553
Generalized Eulerian numbers      571
Generalized harmonic numbers      488
Generalized Liouville function      114
Generalized Mobius function      107 108 135 138
Generalized Mobius functions      134
Generalized Mobius inversion      104
Generalized primes      150
Generalized q-Bernoulli numbers      562
Generalized q-Euler numbers      562
Generalized Ramanujan sum      114
Generalized Stirling numbers      469
Generalized Thabit’s formulae      61
Generalized totient function      269
Generalized totient functions      137
Generating function      460 461 480 483 505 578
Generating functions      474 476 484 570
Genocchi numbers      532
Genocchi numbers of order k      533
Geometrical investigations of congruence theorems      189
Gill’s complexity class      36
Golden number      486
Golomb — Guerin totient function      288
Golubev totient functions      289
Good lattice points modulo composite numbers      345
Graceful graphs      369
Graded poset      146
Gram’s determinant      420
Gravaritm      201
Greatest common divisor      263
Greatest prime divisor of m      255
Greatest prime factor      356
Group of units of the ring $\mathbb{Z}_n$      249
Groups acting on functions      490
Groups acting on graphs      490
Guerin analogue of the Mobius function      122
H-Hypothesis by Schinzel      229
Hall $\pi$-subgroup      158
Hankel contour      523
Hankel integral      581
Hankel matrix      483
Hardy — Littlewood circle method      261
Hardy — Littlewood conjecture      219
Harmonic analysis      415
Harmonic number      466
Harmonic numbers      43 44 472
Haukkanen Mobius function      114
Hausdorff dimension      368
High-speed computers      73
Higher order Bernoulli polynomials      580
Higher order Euler polynomials      558
Highly abundant      347
Highly powerful numbers      334
Hilbert space      185
Hilbert transform      538
Hilbert’s inequality      354
Hoax number      384
Hoheisel — Ingham theorem      380
Holder’s theorem      259
Holiday number      578
Holiday numbers      488
Homogeneous symmetric polynomial      189
Homotopy and homology of finite lattices      148
Hooley’s function      365
Hurwitz zeta function      423
Hyperelliptic equations      507
Hypergeometric functions      525
Hyperharmonic numbers      471
Hyperperfect numbers      50
Hyperplanes      568
Hypothesis H      42
Hypothesis H of Schinzel      222
identities      181 464
Incidence algebra      145
Incidence algebras      139
Incidence function      140
Incidence functions      267
Incidence matrix      268
Incidence ring      140
Independent random variables      511
Indicator      179
Inequalities for $\Phi_n(x)$      261
Inequalities for Stirling numbers      508
Inequalities for the Bernoulli or Euler numbers      575
Inequalities for the r-Stirling numbers,      470
Inequality for $det(S)_f$      273
Infinitary amicable numbers      69
Infinitary convolution      124
Infinitary divisor      48
Infinitary divisors      124
Infinitary harmonic numbers      50
Infinitary Mobius function      124
Infinitary perfect numbers      49
Infinitary sociable numbers      75
Infinitary totient      287
Infinite chess games      390
Infinite dimensional matrix      127
Infinite product      182 424
Infinite recurrences      415
Infinite sums      278 423
Infinitude of primes      180
Inner product      185
Integer partitions in dominance order      148
Integer-perfect numbers      53
Integral ideal      293
Integral ideals      159
Integral product      128
Integral words      151
Intermediate prime divisors      341
Intuitionistic fuzzy theory      148
Inverse problems in Physics      146
Inversion formula      153 160
Inversion formulae      100
Inversion formulas      462
Inversion statistic      481
Inversion theorem      126 145
Inversion theorem of Mobius type      120
Inversions      570
Involutions of permutations      507
Irrational number      411
Irrationality result      254
Irreducibility of polynomials      253
Irreducibility of the cyclotomic polynomial      252
Irreducible polynomial      262 362
Irreducible polynomials      192
Isomorphic classes of objects      186
Iterated Stirling numbers      493
Iterates      75
Iteration      42
Iteration of $\varphi$      195
Iteration of s (n)      429
Iwasawa functions      544
Joint distribution      403
Jordan block      409
Jordan curve      519
Jordan totient      235 275
Jordan totient function      182 214
Jordan — Nagell totient      132 275 276
Jordan-curve      473
Jordan’s totient      106 133 280
Jordan’s totient function      259
jth iterate of the Carmichael function      200
K convolution of incidence functions      143
k-ary divisor      136
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