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| Everest G., van der Poorten A., Shparlinski I. — Recurrence sequences |
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| Предметный указатель |
Cyclic linear code, code-words 247
Cyclic linear code, covering radius 251
Cyclic linear code, generating polynomial 247
Cyclic linear code, Hamming weight 248
Cyclic linear code, Lee weight 248
Cyclic linear code, redundancy 248
Density of prime ideals 52
Density of primitive roots 242
Density of set of prime divisors 74 93 105 106
Density of set of prime maximal divisors 107
Density of super-singular primes 206
Density of unit bits 228
Density, asymptotic 34 53 62 197
Density, positive 62 94 100 137
Density, primitive divisors 104
Dickson polynomial ix
Difference, operator 3
Difference, sequence 63
Difference, sets 105
Differential equations 8
Differential equations, algebraic 7
Differential equations, Grothendieck conjecture 238
Differential equations, homogeneous 71 146
Differential equations, linear 39
Differential equations, linear, polynomial coefficients 41
Differential equations, linear, Skolem — Mahler — Lech Theorem 41
Differential equations, linear, Taylor coefficients 1 7
Differential equations, p-adic 40
Differential equations, partial 218
Differential equations, polynomial 66
Differential equations, rationality, decidability 232
Differential operators 68
Diffie — Hellman key-exchange 247
Digital Signature Algorithm 247
Diophantine, approximation 17 167 196
Diophantine, equations ix 139 151 157—159 161
Diophantine, equations, linear recurrence sequences 157 161
Discrepancy 86 125 127 211
Discrete logarithm 229
Discrete logarithm problem 222 246
Discrete logarithm problem for elliptic curves 164
Discrete root problem 222
Divisibility sequence 70 188
Divisibility sequence, characterization 71
Divisibility sequence, elliptic 71
Division polynomials 165
Dominating roots 5
Dual (character theory) 189
Dual basis 157
Dual sequence 104
Dynamical zeta function ix 61
Dynamical zeta function for  -transformations 60
Dynamical zeta function, hyperbolic systems 61
Edge shift 181
Edge shift, realizable by 182
Effective constant viii
Egyptian fraction equation 161
Eisenstein theorem 14 103
Eisenstein Theorem, bound 103
Elliptic curve 165
Elliptic curve with cyclic reduction infinitely often 52
Elliptic curve, canonical global height 168
Elliptic curve, canonical local height 168
Elliptic curve, discriminant 167
Elliptic curve, division polynomial 165
Elliptic curve, generalised Weierstrass equation 166
Elliptic curve, periods 165
Elliptic curve, singular reduction 168
Elliptic divisibility sequence 163 255
Elliptic divisibility sequence and  168
Elliptic divisibility sequence and discrete logarithms 164
Elliptic divisibility sequence and Somos sequence 9
Elliptic divisibility sequence, defines a point on a curve 167
Elliptic divisibility sequence, generated by a point on a curve 166
Elliptic divisibility sequence, growth rate 167
Elliptic divisibility sequence, not realizable 183
Elliptic divisibility sequence, periodic behaviour 165
Elliptic divisibility sequence, prime apparition 169
Elliptic divisibility sequence, prime apparition heuristics 172
Elliptic divisibility sequence, proper 164
Elliptic divisibility sequence, rank of apparition 164
Elliptic divisibility sequence, singular 163 167
Elliptic divisibility sequence, Zsigmondy's Theorem 169
Elliptic division polynomials 166
Elliptic Lehmer problem 174
Encyclopedia of Integer Sequences xii 12 255
Erdos — Turan inequality 204
Ergodic continued fraction map 8
Ergodic matrix 129
Ergodic theorem 127
Ergodic toral automorphism 189
Euclidean algorithm 13 146 200
Euclidean property 196
Euler — Fermat theorem 94
Euler, binary partition sequence 154 234
Euler, constant 54 95 205
Euler, criterion for quadratic residues 242
Euler, factors 94 172
Euler, function vii 196
Euler, pseudo-prime 242 243
Exceptional units 194
Expansive toral automorphism 189
Exponential, equations 157
Exponential, generator 221
Exponential, linear complexity 219 227
Exponential, polynomial, divisibility 140
Exponential, polynomial, generalized 7
Exponential, polynomial, greatest common divisor 140
Exponential, polynomial, ideal 141
Exponential, polynomial, unique factorization 140
F(S,N) 218
Falting, product theorem 21
Fermat, congruence 241
Fermat, equation 159
Fermat, little theorem 242
Fermat, number 94
Fermat, number, primality test 242
Fermat, number, prime 93 100 255
Fermat, sequence 95
fibonacci 177
Fibonacci, sequence 73 146 148 255
Fibonacci, sequence and graph matchings 177
Fibonacci, sequence and periodic points 181
Fibonacci, sequence, even terms, bisection 93 255
Fibonacci, sequence, locally realizable 187
Fibonacci, sequence, not realizable 181
Fibonacci, sequence, prime terms 95
Fibonacci, sequence, realizable subspace 184
Fibonacci, sequence, squares and cubes in 114
Figures of merit 213
Finite automata 226 240 241
Finite automata, reachability problem 240
Forward prediction 220 222
Forward prediction, 1/M generator 223
Forward prediction, Berlekamp — Massey algorithm 222
Forward prediction, Boyar procedure 223
Forward prediction, linear recurrence 222
Forward prediction, non-linear recurrence sequence 223
Forward prediction, polynomial recurrence equation 223
Forward prediction, power, exponential generator 221
Forward prediction, quadratic generator 223
Forward prediction, truncation 224
Full shift 189
Functional equation 7 232
Functional equation, analogue of Grothendieck conjecture 238
Functional equation, Baum — Sweet sequence 235
Functional equation, m-automatic power series 232
Functional equation, Rudin — Shapiro sequence 234
Functional equation, technique 74
Functional equation, Thue — Morse sequence 234
| Fundamental units 191 194 197
Fundamental units, multiplicative group 198
Fundamental units, multiplicatively independent 201
Fundamental units, positive 158
G(m) 55
G(p) 54
g-ary expansion 132 202
g-ary expansion, normal numbers 218
Gauss, map 8
Gauss, map, invariant measure 8 149
Gaussian period 195 203
Gaussian period, algebraic number fields 195
Gaussian period, finite fields 51
Gaussian period, generates a normal basis 195
Gaussian period, polynomial 205
Gaussian sums 75—77
Generalized exponential polynomial 7
Generalized Lindeloef Hypothesis 122
Generalized power sums 1 3
Generalized power sums, characteristic roots 3
Generalized Riemann hypothesis 50—52 54 55 94 105 108 112 195 243
Generating function 146 231 234 239
Generating function, Baum — Sweet sequence 235
Generating function, cellular automata 241
Generating function, groups 156
Generating function, rationality 156
Generating function, Rudin — Shapiro sequence 234
Generating function, time 239
Generating function, vertical 239
Generating polynomial, cyclic code 247
Generating power series 231
Globally realizable 187 188
Golomb sequence 255
Graph matchings, Fibonacci sequence 177
Graph matchings, Somos-4 sequence 179
Graphical condensation 178
Greatest common divisor, algebraic, analytic 140
Greatest common divisor, Hadamard 140
Greatest common divisor, Ritt 140
Grothendieck conjecture 238
Group automorphism, entropy and Lehmer's problem 30
Group automorphism, periodic points 188 189
Group automorphism, realizable by 182
Group structure of recurrence sequences 4
Growth rate, elliptic divisibility sequence 167
Growth rate, linear recurrence sequence 16 32
Growth rate, periodic points 189
h(f) vii
H(p) 105
H(U,q) 198
Hadamard, greatest common divisor 140
Hadamard, inequality 207
Hadamard, inversion 70
Hadamard, k-th Root Problem 69
Hadamard, operation 65
Hadamard, product 65
Hadamard, product, multi-variate 66
Hadamard, quotient 15
Hadamard, Quotient Problem 15 69
Hadamard, Root Problem 69
Hamming weight 248
Hardy 12
Hardy and Wright 95
Hasse's Theorem 172
Height of a polynomial vii 89
Height, algebraic number 16
Height, canonical 9
Height, naive vii
Heilbronn's conjecture 77
Hermite constant 216
Impulse sequences 2
Index of entry 103
Index of entry, Bell numbers 152
Index of entry, elliptic analogue 164
Index of entry, Lucas numbers 104
Inhomogeneous recurrence relation 2
Initial values 2
Interlacing sequences 67
Inversive sequence 57
Inversive sequence, discrepancy 217
Inversive sequence, lattice test 218
Inversive sequence, maximal period 57
Irregularity index 68
Jacobsthal — Lucas sequence 180 255
Jump complexity profile 228
Kodama's question 205
Kronecker — Hankel, determinant 6
Kronecker — Hankel, matrix 15
L(m,g) 238
Lang 36
Lang, conjecture 18 170 174
Las Vegas algorithm 242
Lattice test 217
Lattice test, inversive generator 218
Lattice test, s-dimensional 217
Least period 181 202
Lee weight 248
Legendre symbol 9
Lehmer — Pierce sequence 30 93 95 180 182
Lehmer, example of small Mahler measure 30
Lehmer, generator 214
Lehmer, generator, discrepancy 216
Lehmer, generator, homogeneous 214
Lehmer, generator, multiplier 214
Lehmer, numbers 23 98 99
Lehmer, primality test 242 243
Lehmer, Problem 30 32 174
Lehmer, problem, elliptic 170 174
Leopoldt Conjecture 37
Linear complexity 72 224 226
Linear complexity and continued fractions 229
Linear complexity profile 226
Linear complexity profile, d-almost perfect 229
Linear complexity profile, perfect 228
Linear complexity, k-error 230
Linear complexity, self-shrunken M-sequence 226
Linear congruencial generator 214
Linear congruencial generator, discrepancy 216
Linear congruencial generator, elliptic analogue 221
Linear congruencial generator, homogeneous 214
Linear forms in logarithms xi 15 18 32 33 96 133
Linear forms in logarithms, multiplicative form 16
Linear recurrence relation, homogeneous 1
Linear recurrence relation, order 1
Linear recurrence sequence 1 226
Linear recurrence sequence and linear differential equations 7
Linear recurrence sequence and rational functions 6
Linear recurrence sequence and traces 3
Linear recurrence sequence as a generalized power sum 3
Linear recurrence sequence, affine equations in 71
Linear recurrence sequence, arithmetic subsequence 5
Linear recurrence sequence, binary, ternary 2
Linear recurrence sequence, character sums 75
Linear recurrence sequence, characteristic polynomial 1
Linear recurrence sequence, degenerate, non-degenerate 5
Linear recurrence sequence, density of prime divisors 105
Linear recurrence sequence, density of prime maximal divisors 107
Linear recurrence sequence, divisors 4
Linear recurrence sequence, exceptional 38
Linear recurrence sequence, group structure 4
Linear recurrence sequence, group structure, double root 4
Linear recurrence sequence, group structure, torsion 106
Linear recurrence sequence, growth 16 32
Linear recurrence sequence, Hadamard operation 66
Linear recurrence sequence, initial values 2
Linear recurrence sequence, many variables 10
Linear recurrence sequence, matrix powers 6
Linear recurrence sequence, minimal polynomial 1
Linear recurrence sequence, multipliers 49
Linear recurrence sequence, number of zeros 87
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