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| Everest G., van der Poorten A., Shparlinski I. — Recurrence sequences |
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| Предметный указатель |
Linear recurrence sequence, order 1
Linear recurrence sequence, periodic structure 46
Linear recurrence sequence, powers in 113
Linear recurrence sequence, prime divisors 93
Linear recurrence sequence, reduction to non-degenerate 5
Linear recurrence sequence, restricted period 49
Linear recurrence sequence, set of solutions 2
Linear recurrence sequence, squares and cubes in 114
Linear recurrence sequence, sum and product 65
Linear recurrence sequence, zeros 31
Linearized polynomial 57
Linnik, constant 243
Linnik, Theorem 59
Liouville, number 133
Liouville, Theorem 147
ln x vii
Locally realizable 186
Locally realizable, everywhere 187
Log x vii
Lucas, numbers 23 98 99 103 106 111 112 115 163 180 184 255
Lucas, numbers and periodic points 180
Lucas, numbers, index of entry 104
Lucas, numbers, primitive divisors 104
Lucas, numbers, primitive power divisors 104
Lucas, pseudo-prime 243
Lyness sequence 9
M(A) 26
m(a,c) 26
m(f) 60
M(n) 31
m-automatic 231
m-automatic, algebraic irrationals are not 232
m-automatic, sequences over finite fields 232
m-automaton 231
m-automaton, acceptance set 231
m-automaton, initial state 231
m-automaton, language 231
M-kernel 232
m-kernel, finiteness characterizes m-automatic 232
M-sequences 45
M-sequences in residue rings 47
M-sequences over finite fields 46
M-sequences over Galois rings 46
M-sequences, shrinking generator 72
Mahler, 3/2-problem 61 134 206
Mahler, m-functions 232
Mahler, measure 29 30 168
Mahler, measure, entropy 30
Mahler, measure, smallest known 30
Matrix, almost integer 129
Matrix, ergodic 129
Max sequence 63
Maximal divisor 107
Maximal period of matrices 47
Maximal period, construction of sequences 47
Maximal period, modulo composites 52
Maximal period, modulo prime powers 47
MergeSort algorithm, complexity 234
Mersenne, number 100 149
Mersenne, prime 53 93 156 189 255
Mersenne, sequence 180
Mersenne, sequence, prime heuristics 94
Merten's Theorem 95 172
Minimal, non-mixing shapes 141
Minimal, polynomial 1
Minimal, quadratic residue 55
Mixing for  -actions 43 141 157
Modulus of a linear cellular automata 49
Modulus of a pseudo-random number generator 211
Moebius function vii
Monte Carlo method 220
Multiplication-with-carry sequence 217
Multiplicative character 86
Multiplicative character, order 86
Multiplicative function 71
Multiplicative order 45
Multiplicity 26
Multiplicity, low order sequences 27
Multiplicity, lower bounds 28
Multiplicity, non-uniform bounds 29
Multiplicity, total 26 38
Multiplicity, uniform bounds 27
Multipliers 49
Multipliers, group of 49
N(n) 31
N(p) 55
n-sparse polynomials 139
n-sparse rational functions 139
Naor — Reingold pseudo-random number generator 85
Near-Euclidean property 196
Non-linear recurrence relations 8
Non-linear recurrence relations, correlation 251
Nondegeneracy 5
Norm of a polynomial 142
Norm-form equation 157 158
Normal, basis 191
Normal, extension 191
Normal, number 86
Normal, number to base g 102
Normal, number, absolutely 127
Normal, periodic systems 130
Normal, sequences of signs 218
Normality 127
NP-hard problem 245
Orbit Problem 246
Orbit Problem for linear recurrences 240
Orbit Problem for matrix groups 246
Orbit Problem over  246
Orbit Problem over a finite field 246
Order of a character 86
Order of a linear recurrence sequence 1
Order, p-adic vii
P(k) vii
p-adic analytic function 13
p-adic convergence 12
p-adic differential equations 40
p-adic expansion 12
p-adic logarithms 25
p-adic meromorphic function 13
p-Adic metric 12
p-adic rationals 12
p-adic subspace theorem 20
p-adic valuation 12
p-adic Weierstrass preparation theorem xi 13
P-binomial coefficients 70
P-part of a sequence 186
Painleve equation 8
Paper-folding sequence 235
Paper-folding sequence, 2-automatic 235
Paper-folding sequence, Fourier transform 236
Pattern counting function 236
Pattern sequence 235
Pattern sequence, associated trigonometric polynomial 236
per(f) 46
Perfect matching 177
Perfect matching, Aztec diamonds 178
Perfect matching, Somos-4 sequence 179
Perfectly cyclic 59
Period 50
Period of a polynomial 46
Period of a sequence 45
Period of add-with-carry sequence 56
Period of doubly exponential sequence 55
Period of m-dimensional sequences 59
Period of matrices 47
Period of shrunken sequences 55
Period, in finitely generated groups 53
Period, modulo p 50
Period, modulo p, lower bounds on average 53
Period, relation to linear recurrence sequence 54
| Periodic points 179
Periodic points for quadratic polynomials 59
Periodic points in dynamical systems 177
Periodic points, automorphism of solenoid 189
Periodic points, edge shifts 181
Periodic points, Fibonacci sequence 181
Periodic points, group endomorphism 188
Periodic points, group endomorphisms 189
Periodic points, growth rate 189
Periodic points, Jacobsthal-Lucas sequence 180
Periodic points, Lucas sequence 180
Periodic points, Mersenne sequence 180
Periodic points, readability in rate 189
Periodic points, realizable in rate 189
Periodic points, toral automorphism 189
Permutation polynomial 218
Pillai equation 160
Pisot sequence 255
Pisot — Varadarajan number 60
Pollard's  -method 244
Polya operator 68
Polynomial, Artin — Schreier 152 194
Polynomial, as linear recurrence 139
Polynomial, Bernoulli 153
Polynomial, black-box 144
Polynomial, cycles 201
Polynomial, division 164 165
Polynomial, factorization 139
Polynomial, Gaussian period 205
Polynomial, irreducible in the strong sense 141
Polynomial, multi-variate factorization 140
Polynomial, never realizable 183
Polynomial, reciprocal 93
Polynomial, sparse 75 141
Positive unit 158
Power generator 85 217 221
Predictability problem 220
Primality test 241
Primality test, certifying 242
Primality test, deterministic 153 242 243
Primality test, Fermat's Little Theorem 242
Primality test, Lehmer 242
Primality test, Mersenne numbers 243
Prime number theorem x 94 188
Prime Number Theorem, dynamical analogue 61
Prime terms in linear recurrences 93
Prime terms, elliptic divisibility sequence 169
Prime terms, Fibonacci sequence 95
Primitive divisor 93 100 103 104
Primitive divisor, composite 104
Primitive divisor, elliptic divisibility sequence 169
Primitive divisor, Lucas and Lehmer sequence 104
Primitive matrix 182
Primitive normal basis 191
Primitive polynomial 57
Primitive power divisors 104
Primitive root 51 139 202 242
Primitive root in arithmetic progression 51
Primitive root, analogues for composite modulus 52
Primitive root, least 54
Primitive root, modulo prime powers 47
Primitive root, unconditional results 51
Product formula 12 14
Pseudo-prime, Euler 242
Pseudo-prime, Lucas 243
Pseudo-prime, strong to the base a 243
Pseudo-prime, to the base a 241
Pseudo-random number generator 211
Pseudo-random number generator, complexity 220
Pseudo-random number generator, Naor — Reingold 85 221
Pseudo-random numbers 226
Pseudo-random sequence of digits 218
Purely periodic 59
Purely periodic, sequence 45
PV-number 60 129
PV-number, special 60
PV-number, totally positive 135
Q(k) vii
q-generalizations 7
Quadratic generator, discrepancy 217
Quadratic generator, forward prediction 223
Quadratic irrationality 101
Quadratic irrationality, continued fraction 8 145
Quadratic irrationality, period of continued fraction 147
Quadratic number fields, fundamental units 191
Quadratic polynomial, iteration 58
Quadratic polynomial, periodic points 59
Quadratic residue 59
Quadratic residue, Euler's criterion 242
Quadratic sequence 124
Quadratic sequence, maximal period 57
Quadratic sequences 56
Quantum convolution 67
Quasi-random number 219
Quasi-random number,  -nets 220
Quasihyperbolic toral automorphism 189
Quicksort algorithm 244
R(t,p,a) 203
R(U,q,h) 198
Rabin primes 222
Ramanujan 170
Ramanujan,  -function 150 255
Ramanujan, -function, recurrence equation 150
Rank of apparition 164
Rational function vii
Rational function, differential operator 68
Rational function, dynamical zeta function 61
Rational function, Eisenstein Theorem 103
Rational function, linear recurrence sequence 6
Rational function, modulo composites 56
Rational function, periodic points 59
Rational function, power series 6
Rational function, recognizing 14
Rational function, several variable 10
Reach 179
Realizable sequence 181
Realizable sequence, algebraically 188
Realizable sequence, binary recurrence 184
Realizable sequence, globally 187
Realizable sequence, in rate 189
Realizable sequence, locally 186
Realizable sequence, prime appearance 188
Realizable sequence, sum and product 182
Reciprocal polynomial 6 93
Reciprocal polynomial, Mahler measure 30
Recurrence relation, elliptic 9 163
Recurrence relation, inhomogeneous 2
Recurrence relation, non-linear 8
Recurrence sequence on elliptic curves 42
Recurrence sequence, bilinear 11
Recurrence sequence, elliptic 163
Recurrence sequence, group structure 4
Recurrence sequence, growth 31
Recurrence sequence, q-generalization 7 102
Recurrence sequence, shrinking 71
Recurrence sequence, transcendence theory 72
Recurrence sequence, zeros 31
Recurrence sequence, zeros in a segment 34
Regular numeration system 238
Regular sequences 233
Restricted period 49
Restricted period, over finite rings 49
Riesel number 255
Riesz — Raikov Theorem 136
Ritt greatest common divisor 140
Robinson's question 207
Roth theorem 17 32 95 114 147
Roth Theorem, p-adic 32
RSA-cryptosystem 222
RSA-cryptosystem, continued fractions 222
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