@article{JTNB_1992__4_1_75_0, author = {Tamura, Jun-Ichi}, title = {Transcendental numbers having explicit $g$-adic and {Jacobi-Perron} expansions}, journal = {S\'eminaire de th\'eorie des nombres de Bordeaux}, pages = {75--95}, publisher = {Universit\'e Bordeaux I}, volume = {Ser. 2, 4}, number = {1}, year = {1992}, mrnumber = {1183919}, zbl = {0763.11029}, language = {en}, url = {http://www.numdam.org/item/JTNB_1992__4_1_75_0/} }
TY - JOUR AU - Tamura, Jun-Ichi TI - Transcendental numbers having explicit $g$-adic and Jacobi-Perron expansions JO - Séminaire de théorie des nombres de Bordeaux PY - 1992 SP - 75 EP - 95 VL - 4 IS - 1 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1992__4_1_75_0/ LA - en ID - JTNB_1992__4_1_75_0 ER -
Tamura, Jun-Ichi. Transcendental numbers having explicit $g$-adic and Jacobi-Perron expansions. Séminaire de théorie des nombres de Bordeaux, Série 2, Tome 4 (1992) no. 1, pp. 75-95. http://www.numdam.org/item/JTNB_1992__4_1_75_0/
[1] A remarkable class of continued fractions, Proc. Amer. Math. Soc. 65 (1977), 194-198. | MR | Zbl
and ,[2] Automates finis en théorie des nombres, Expo. Math. 5 (1987), 239-266. | MR | Zbl
,[3] The Jacobi-Perron Algorithm, its Theory and Application, Lect. Notes in Math. 207, Springer-Verlag, (1971). | MR | Zbl
,[4] Über die Transzendenz gewisser dyadischer Brüche, Math. Ann. 96 (1927), 367-377. | JFM | MR
,[5] Über eine Klasse reeler transzendenter Zahlen mit explicit angebbarer g-adischer und Kettenbruch-Entwicklung, J. reine angew. Math 318 (1980), 110-119. | MR | Zbl
,[6] Some functions related to Fibonacci and Lucas representations,, The Theory of Arithmetic FunctionsLect. Notes in Math. 251 Springer-Verlag, 1972, 71-102. | MR | Zbl
, , and ,[7] O nekotorykh klassakh transcendentnykh cisel, Mat. Zametki, Tom 12, No 2 (1972), 149-154 = Some classes of transcentental numbers, Math. Notes 12 (1972), 524-527. | MR | Zbl
,[8] A series and its associated continued fraction, Proc. Amer. Math. Soc. 63 (1977), 29-32. | MR | Zbl
,[9] Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400. | JFM
,[10] Systems of numeration, Amer. Math. Monthly 92 (1985), 105-114. | MR | Zbl
,[11] Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 198. | Zbl
and ,[12] The Art of Computer Programming, Vol. III (Sorting and Searching), Addison Wesley, 1973, pp. 269-270, pp. 286-287, and pp. 647-648. | MR | Zbl
,[13] Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366. | JFM | MR
,[14] Racional'nye approksimacii i ortogonal'nost' (in Russian), Nauka, 1988, 168-175.
and ,[15] Arithmetical properties of certain power series, (1990), to appear in J. Number Theory. | Zbl
, and ,[16] Algoritm Jacobi-Perrona i sovmestnoe priblizenie funkcij (in Russian), Mat. Sbornik 114 (156) no. 2 (1982), 322-333. | MR | Zbl
,[17] Problems and Theorems in Analysis II, Springer-Verlag, 1976. | Zbl
and ,[18] Nombres algébriques et substitutions, Bull. Soc. Math. France 110 (1982), 147-178. | Numdam | MR | Zbl
,[19] A generalization of automatic sequences, Theor. Comput. Sci. 61 (1988), 1-16. | MR | Zbl
,[20] A Handbook of Integer Sequences, Academic Press, 1973. | Zbl
,[21] Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull. 19 (1976), 473-482. | MR | Zbl
,[22] Représentation des nombres naturels par une somme de nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège 41 (1972), 179-182. | MR | Zbl
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