Everest G., van der Poorten A., Shparlinski I. — Recurrence sequences :: Электронная библиотека попечительского совета мехмата МГУ

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Everest G., van der Poorten A., Shparlinski I. — Recurrence sequences

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Название: Recurrence sequences

Авторы: Everest G., van der Poorten A., Shparlinski I.

Аннотация:

Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 323

Добавлена в каталог: 21.08.2005

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Предметный указатель

$(\mathcal{R},m)$ -regular sequences      232
$A(\mathbb{K},q)$       196
$a\ast b$       66
$a\odot b$       67
$a_{+}(x)$       93
$a_{-}(x)$       93
$a_{bs}$       236
$a_{rs}$       234
$a_{s}(x)$       71
$A_{tm}$       234
$B_{k,s}(a(0),\lambda,M)$       224
$B_{n}$       187
$Cycl_{\mathcal{R}}(F)$       58
$C_{a,\lambda,p}(N)$       244
$E(M,k,\varepsilon)$       225
$e_{P}(x)$       233
$Fix_{n}(T)$       180
$f^{-}$       6
$f^{\lambda}$       70
$G_{H}(E,F)$       140
$G_{R}(E,F)$       140
$G_{\mu}$       49
$H_{m,p}(a)$       208
$H_{m}$       3
$I_{a,\lambda,p}(N,H)$       244
$I_{m}$ , $I_{m}(a)$       103
$J(q,n,\Delta)$       253
$J_{a}(h)$       228
$Ker_{a,m}$       232
$L(\mathcal{K},q)$       196
$ln^{(n)}$       112
$L\Pi_{\tau}$ -nets      220
$L^{+}_{x}$       99
$L^{-}_{x}$       99
$L_{a}(N)$       248
$L_{n}(T)$       181
$L_{p}(N)$       198
$M(\mathbb{K},V)$       201
$M(\mathbb{K},V,q)$       201
$M(\vartheta)$       30
$M_{j}(m,p)$       208
$M_{p}$       93
$N_{p,F,k}(n)$       68
$N_{p,s,k}(n)$       68
$N_{p}(s,n)$       67
$N_{q}(\alpha)$       196
$ord_{p}z$       vii
$O_{n}(T)$       181
$p(\lambda)$       51
$P_{a}(N)$       93
$Q_{a,p}(N,H)$       120
$Q_{a}(N)$       62
$R_{a,g,p}(N,H)$       122
$R_{n}(q)$       141
$r_{s}(f,m,p)$       212
$S(\lambda,N)$       85
$S_{x}$       147 191
$T(\ell)$       205
$T_{j}(p,s,g)$       202
$T_{k}$       82
$T_{m}(N,I)$       120
$T_{n}(t,q)$       205
$T_{N}(\vartheta_{1},...,\vartheta_{s})$       117
$T_{\alpha}(N,\Delta)$       149
$t_{\lambda}(p)$       50
$T_{\mathcal{R}}(F)$       58
$W_{a}(N)$       248
$W_{m}$       231
$W_{s}(\delta,M)$       216
$Z_{s,t,\alpha}$       135
$Z_{s,t,\alpha}$ -numbers      135
$Z_{t,\alpha}$       134
$Z_{t,\alpha}$ -numbers      134
$\delta(a)$       107
$\delta_{ij}$       vii
$\ell_{p}(n)$       198
$\hat{h}(Q)$       168
$\Lambda_{q^{\ast}}$       196
$\Lambda_{q}$       196
$\leftrightarrow$       4
$\mathbb{C}$       vii
$\mathbb{C}_{p}$       vii
$\mathbb{F}^{\ast}_{q}$       vii
$\mathbb{F}_{q}$       vii
$\mathbb{K}_{z}\{\mathcal{W}\}$       140
$\mathbb{N}$       vii
$\mathbb{P}$       vii
$\mathbb{Q}$       vii
$\mathbb{Q}_{p}$       vii
$\mathbb{R}$       vii
$\mathbb{Z}$       vii
$\mathbb{Z}_{+}$       vii
$\mathbb{Z}_{p}$       vii
$\mathbb{Z}_{\mathbb{K}}$       vii
$\mathcal{A}(d,m,a)$       155
$\mathcal{G}(f)$       4
$\mathcal{G}(\Omega,V)$       201
$\mathcal{G}(\Omega,V,q)$       201
$\mathcal{L}$       231
$\mathcal{L}(f)$       2
$\mathcal{L}^{\ast}(f)$       2
$\mathcal{L}^{\ast}_{a}$       226
$\mathcal{L}_{a}$       226
$\mathcal{L}_{a}(k,h)$       230
$\mathcal{R}$       vii
$\mathcal{R}((X))$       vii
$\mathcal{R}(X)$       vii
$\mathcal{R}[X]$       vii
$\mathcal{R}[[X]]$       vii
$\mathfrak{B}_{h}$       198
$\mu(k)$       vii
$\mu_{0}(n,\mathcal{R})$ , $\mu(n,\mathcal{R})$       26
$\nu(k)$       vii
$\nu_{\ast}(m)$       208
$\Omega(k)$       109
$\omega(M,N)$       95
$\omega(N)$       95
$\Omega(\alpha)$       135
$\omega_{s}(\lambda, M)$       215
$\overline{\mathbb{F}}$       vii
$\pi(x)$       vii
$\pi_{a}(N)$       105
$\rho_{s}(\lambda,M)$       214
$\sigma(k)$       vii
$\sigma(z)$       165
$\tau(K)$       vii
$\tau(p,s,g)$       202
$\varepsilon$       vii
$\varphi(k)$       vii
$\zeta_{f}(z)$       60
$|\cdot|_{p}$       12
(m,g)-automatic      238
(m,g)-automatic, real number      238
A(S, M, N)      98
ABC-Conjecture      22 98
Absolutely normal number      127
Absolutely normal number, almost all reals      128
Absolutely normal number, explicit construction      131
Ackerman's Function      11 255
Add-with-carry sequence      56 217
Add-with-carry sequence, period      56
Additive function      71
Aliquot sequence      63 255
Aliquot sequence, arbitrarily long      63
Almost all      viii
Almost periodic sequence      235
Anomalous prime      170
Anomalous prime, finitely many      172
Arithmetic progression      5 26 34
Arithmetic progression of zeros      25

Arithmetic progression, primes      51 206
Arithmetic progression, primitive root in      51
Artin — Schreier polynomial      152 194
Artin, conjecture      49—52 157 189 196 199 200 224
Artin, conjecture for function fields      52
Artin, conjecture for function fields on elliptic curves      52
Artin, conjecture in number fields      52 107
Artin, conjecture on average      50
Artin, conjecture on CM curves      52
Artin, conjecture on elliptic curves      52
Artin, conjecture, elliptic analogue      51
Artin, constant      50
Artin, integers      195
Autocorrelation function      251
Automaton, accepted word      231
Automaton, cellular      240
Automaton, circular shape      239
Automaton, finite      232
Automaton, finite, binomial coefficients      241
Automaton, minimal size      237
Automaton, to compute a function      237
Aztec diamonds      178
Backward prediction      220
Backward prediction, cellular automata      241
Backward prediction, power, exponential generator      222
Baker's theorem      16 20
Baum — Sweet sequence      234 236
Baum — Sweet sequence, generating function      235
BCH-code      253
Bell numbers      150
Bell numbers, index of entry      152
Bell numbers, modulo composites      156
Bell numbers, recurrent congruence      151
Berlekamp — Massey algorithm      222 226 247
Bernoulli, denominators      188 255
Bernoulli, normal sequence      218
Bernoulli, numbers      187
Bernoulli, numbers, Kummer congruences      187
Bernoulli, numbers, realizable      187
Bernoulli, numerators      188 255
Bernoulli, polynomials      153
Berstel's sequence      28 31 38 255
Bilinear, recurrence sequence      9 11
Bilinear, recurrence sequence, binary, ternary      11
Binary length sequence      233 255
Binary partition sequences      153 255
Birthday paradox      244
Black-box      144
Blahut algorithm      222 226
Blum, Blum and Shub generator      58 221 223
Boolean functions      245
Borel's theorem      14
Canonical height      9 42
Canonical height, analogue of Lehmer problem      173 174
Canonical height, functoriality      168
Canonical height, global      168
Canonical height, Lang's conjecture      174
Canonical height, local      168
Canonical height, sum of local heights      168
Carmichael number      241 242
Catalan, conjecture      255
Catalan, equation      157 159
Cellular automata      231 238
Cellular automata as 2-dimensional recurrence      239
Cellular automata, backward prediction      241
Cellular automata, boundary rule      239
Cellular automata, class membership      240
Cellular automata, fractal orbit portraits      241
Cellular automata, generating function      241
Cellular automata, higher-dimensional      241
Cellular automata, initial configuration      239
Cellular automata, linear      239
Cellular automata, probabilistic      241
Cellular automata, reachability problem      240
Cellular automata, time, vertical generating function      239
Cellular automata, transition rule      239
Character of $\mathbb{F}_{q}$       75
Character sums      75 76
Character sums over $\mathbb{C}$       85
Character sums, upper bounds on average      83
Character sums, upper bounds, algebraic number fields      76
Character sums, upper bounds, finitely generated groups      76
Character sums, upper bounds, incomplete sums      77
Character sums, upper bounds, multiplicative characters      86
Character sums, upper bounds, positive characteristic      75
Character sums, upper bounds, rationals      77
Character sums, Weil bound      143
Character, multiplicative      86
Character, quadratic      51
Character, theory (Pontryagin)      187
Characteristic polynomial      xi 1 16
Characteristic polynomial and rational functions      6
Characteristic polynomial, Berstel's sequence      28
Characteristic polynomial, discriminant      36
Characteristic polynomial, M-sequence      46
Characteristic polynomial, matrix powers      6
Characteristic polynomial, minimal length      1
Characteristic polynomial, possible linear recurrence sequences      2
Characteristic polynomial, product of sequences      2
Characteristic polynomial, sequence of traces      3
Characteristic polynomial, unique dominating root      5
Checking polynomial      247 249
Chinese remainder theorem      49 139
Class number, minus part      202
Code-words      247
Code-words, bound for number      249
Code-words, minimum weight      250
Code-words, number of different weights      252
Coefficient ring      1
Collatz sequence      8 61
Collatz sequence, generalization      62
Collatz sequence, periodic structure      45
Completely uniformly distributed      127
Complexity profile, jump      228
Complexity profile, linear      226 229
Complexity profile, linear, d-almost perfect      230
Complexity profile, linear, perfect      228
Composition and Bell numbers      150
Composition of exponential polynomials      102
Composition of functions      180
Composition of linear recurrence sequences      66
Continued fraction      8 91 101 137 145 146
Continued fraction of power series      147
Continued fraction over field of formal Laurent series      228
Continued fraction, almost every real      8
Continued fraction, bounded partial quotients      148
Continued fraction, Fibonacci sequence      148
Continued fraction, Gauss measure      149
Continued fraction, length      146
Continued fraction, multiples of irrationals      137
Continued fraction, normal expansion      149
Continued fraction, normal numbers      132 149
Continued fraction, numerators and denominators      145
Continued fraction, quadratic irrational      145
Convolution of linear recurrence sequences      67
Convolution, quantum      67
Convolution, sequences with polynomial coefficients      67
Coordinate sequence      56 67
Coordinate sequence, order      68
Coordinate sequence, period      56
Correlation, cyclic linear code      251
Correlation, function      251
Correlation, non-linear recurrence sequences      251
Correlation, small      251
Cryptography      216 247
Cryptography, timed-release      247
Cullen numbers      94 255
Cycles, polynomial      201
Cyclic linear code      247
Cyclic linear code, checking polynomial      247

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