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| Rockett A.M., Szusz P. — Continued Fractions |
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| Предметный указатель |
Adams, William W. 36
Approximation by intermediate convergents 112
Approximation by non-convergents 112
Approximation, asymmetric 110
Approximation, homogeneous 19
Approximation, inhomogeneous 116 136
Auxiliary convergent 36
Babenko, K. L 166
Barnes, E. S. 136
Beppo Levi Theorem 141
Bernstein, Felix 169
Best approximation 17 19
Best approximation, arc sine law 167
Best approximation, first kind 36
Best approximation, second kind 36
Billingsley, Patrick viii 167
Borel sets 137
Borel — Cantelli lemma 140
Borel, Emile 135
Brillhart, John 135
Brouncker, William 64
Calendar construction 60 134
Cantor set 72
Cantor set, sum 73
Cantor set, sum, direct construction 135
Cassels, J. W. S. 17 136
Cattle problem of Archimedes 134
Central limit theorem 167
Ceulen, Johannes van 134
Characteristic equation 58
Charves, M. 41
Chebyshev’s inequality 145
Chinese remainder theorem 51
Conjugate of a quadratic surd 43
Continued fraction 1
Continued fraction with bounded digits 72 74
Continued fraction, complete quotient 4
Continued fraction, complex partial quotient 17
Continued fraction, convergent 1
Continued fraction, convergent, of a reciprocal 10
Continued fraction, general 58
Continued fraction, partial quotient 1
Continued fraction, regular 3
Continued fraction, to the nearest integer 18
Continued fraction, transformation 8
Convergent 1
Convergent, auxiliary 36
Convergent, denominator 2
Convergent, intermediate 36
Convergent, numerator 2
Convergent, principal 36
Convergent, quasi- 36
Cousins, Frank W. 134
Cusick, Thomas W. 135 136
Davenport, Harold 37 135 136
Descombes, Roger 37 136
Dickson, Leonard Eugene 17 18 134 135 136
Difference 9
Diophantine approximation 19
Diophantine approximation, homogeneous 19
Diophantine approximation, inhomogeneous 116 136
Diophantine approximation, metrical 169
Durner, Alexander viii
Dutka, Jacques 134
e 13
e approximation 30
e approximation by convergents 37
e approximation by non-convergents 115
e linear recurrence (example) 53
Equivalent, quadratic forms 84
Equivalent, real numbers 6
Erdos, Paul 175
Ergodic theorem 167
Euclidean algorithm 17
Euler, Leonhard 18 40 51 64 66 69
Event 137
Event, probability 137
Event, probability one 138
Event, probability zero 137
Farey sequence 134 136
Fermat, equation 134
Fermat, Pierre de 64
Fermat, sum of two squares 69
Fibonacci sequence 12 54
Fibonacci sequence, Ostrowski representation 24
Flahive, Mary E. 135 136
Forder, H. G. 135
Fraenkel, Aviezri S. 36
Freiman, G. A. 136
G 11 39
g approximation by by non-convergents 113
g approximation by convergents 80—81
g approximation by inhomogeneous 122 130
Galois, Evariste 45
Gauss — Kuzmin theorem 151
Gauss, K. F. 135 151 166
Gear ratio problem 59
Gear ratio problem, general 64
Girard, Albert 69
Goldbach, Christian 64
Golden ratio 11 18 39
Grace, J. H. 36
h, conjugate of g 12
Halberstam, Heini 134
Hall, Jr., Marshall 78 135
Hall, ray 136
Hall, theorem 72
Hardy, G. H. vii 17 58 136
Hermite, Charles 69 71 135
Hickerson, Dean R. 58
Homogeneous problem 19
Hua, Loo-keng 134
Hurwitz, Adolph vii 17 80 135
Huygens, Christiaan 59 134
Inhomogeneous approximation 32 37 116
Inhomogeneous approximation, Khintchine 122
Inhomogeneous approximation, Minkowski 117
Intermediate convergent 36
Interval of order n 138
Inverse period 46
Ito, Shunji 18
Jacobsthal, E. 135
Jones, William B. vii 17
Jurev, S. P. 166
Kac, Mark viii
Khintchine — Levy constant 164
Khintchine — Levy, theorem 163
Khintchine, A. Ya. vii 17 36 122 136 146 160 163 167 170
Khintchine, constant 163
Khintchine, theorem 160
Koksma, J. F. 136
Kolmogorov-type inequality 150 174
Kuzmin, R. O. 152
Lagrange, chain of forms 92
Lagrange, Joseph-Louis 22 41 50 134
Lagrange, spectrum 84
| Lagrange, spectrum, alternative definition 93
Landau order notation ix
Lang, Serge 36
Laplace, Pierre-Simon 151 166
Lattice point 131
Law of iterated logarithm 167
Law of Large Numbers 145
Law of Large Numbers, strong 148
Law of large numbers, strong, with error term 149
Law of large numbers, weak 146
Lebesgue dominated convergence theorem 141
Lebesgue measure 137
Lebesgue — Stieltjes integral 143
Legendre, Adrien-Marie 22 36 46 69 135
Lekkerkerker, C. K. 36
LeVeque, William J. vii 17 36 58 134 135 136 175 176
Levy, Paul viii 18 152 156 163 167
Linear recurrence 53 58
Mahler, K. 136
Markov, A. A. 146
Markov, chain 104 105
Markov, form 103
Markov, number 101
Markov, spectrum 85
Markov, spectrum, alternative definition 93
Markov, triple 101
Markov, triple, complete 103
Markov, triple, neighbors 102
Markov, triple, non-singular 101
Markov, triple, singular 101
Markowsky, George 18
Mathews, Jerold 134
Minkowski, Hermann 117 131
Modular group 17
Mordell, Louis Joel 131
Niven, Ivan, vii, viii 17 58 135
Ostrowski, Alexander 24 36
Ostrowski, algorithm 24
Ostrowski, representation 24 36 37
Ostrowski, representation negative integer 32
Ostrowski, representation using Fibonacci numbers 24
Ostrowski, representation using g 24 36
Partial quotient 1
Partial quotient, arithmetic mean 142
Partial quotient, bounded 138
Partial quotient, geometric mean 163
Partial quotient, real valued 111
Partial quotient, relative frequency 162
Partial quotient, weakly dependent 159
Pell, John 64 134
Pell’s equation vii 31 64 69
Periodic continued fraction 39
Periodic continued fraction, examples 44—45 47—49
Periodic continued fraction, initial block 39
Periodic continued fraction, inverse period 46
Periodic continued fraction, period 39
Periodic continued fraction, period length 49
Periodic continued fraction, purely 39
Periodic continued fraction, repeating block 39
Perron, Oskar vii 17 18 36 58 135
Philipp, Walter viii 167 176
Piper’s algorithm 134
Planetarium 59
Podsypanin, E. V. 58
Principal convergent 36
Quadratic form, (real, indefinite binary) 84
Quadratic form, chain 89
Quadratic form, discriminant 84
Quadratic form, equivalent 84
Quadratic form, inverse equivalence 91
Quadratic form, minima 18 84
Quadratic form, neighbor 88
Quadratic form, properly represented number 86
Quadratic form, reduced 86
Quadratic form, roots 84
Quadratic residue 51
Quadratic surd 39
Quadratic surd, conjugate 43
Quadratic surd, discriminant 39
Quadratic surd, reduced 45
Quasi-convergent 36
Rademacher, Hans 17
Random variable 141
Random variable, density function 143
Random variable, distribution function 143
Random variable, expectation 141
Random variable, joint distribution function 144
Random variable, mixing sequence 167
Random variable, mutually independent 166
Random variable, n-th moment 143
Random variable, pairwise independent 144
Random variable, totally independent 144
Random variable, variance 144
Random variable, weakly dependent 144
Remak, Robert 136
Renyi, Alfred viii 166
Revesz, Pal viii 166
Rieger, Georg Johann 18
Rockett, Andrew M. 18 37 135
Ryll-Nardzewski, Czeslaw viii 167
Schmidt, Wolfgang M. 175 176
Segre, Beniamino 110
Series, Caroline 136 167
Serre, Jean-Pierre 17
Serret, J. A. 135
Set,  -algebra 137
Set, almost everywhere 138
Set, Borel 137
Set, complement 137
Set, measure zero 137
Set, pairwise disjoint 137
Shanks, Daniel 135
Simson, Robert 18
Sos, Vera T. 37
Sprindzuk, Vladimir G. 176
Stout, William 167
Swinnerton-Dyer, H. P. F. 136
Szekeres, George 130 136
Szusz, Peter 37 135 136 166 176
t-expansion 32 116 136
Tanaka, Shigeru 18
Ternary notation 72
Thron, Wolfgang J. vii 17
Truncation 146
Unimodular, relation between t and  6 41
Unimodular, transformation 6
Uspensky, J. V. 166
Vahlen, K. Th. 135
Volkmann, Bodo viii
Wall, H. S. vii 17
Wallis, John 64
Waterman, Michael S. 166
Weil, Andre viii 134 136
Wirsing , Eduard 166
Wolffing, E. viii
Wright, E. M. vii 17 58 135 136
Zuckerman, H. S. vii 17 58 135
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