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.
@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://archive.numdam.org/item/JTNB_1992__4_1_75_0/}
}
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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://archive.numdam.org/item/JTNB_1992__4_1_75_0/

[1] Adams, W.W. and Davison, J.L., A remarkable class of continued fractions, Proc. Amer. Math. Soc. 65 (1977), 194-198. | MR | Zbl

[2] Allouche, J.-P., Automates finis en théorie des nombres, Expo. Math. 5 (1987), 239-266. | MR | Zbl

[3] Berstein L., The Jacobi-Perron Algorithm, its Theory and Application, Lect. Notes in Math. 207, Springer-Verlag, (1971). | MR | Zbl

[4] Böhmer, P.E., Über die Transzendenz gewisser dyadischer Brüche, Math. Ann. 96 (1927), 367-377. | JFM | MR

[5] Bundschuh, P.E., 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] Carlitz, L., Hoggatt, V.E., and Scoville R., Some functions related to Fibonacci and Lucas representations,, The Theory of Arithmetic FunctionsLect. Notes in Math. 251 Springer-Verlag, 1972, 71-102. | MR | Zbl

[7] Danilov, L.V., 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] Davison, J.L., A series and its associated continued fraction, Proc. Amer. Math. Soc. 63 (1977), 29-32. | MR | Zbl

[9] Fatou, P., Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400. | JFM

[10] Fraenkel, A.S., Systems of numeration, Amer. Math. Monthly 92 (1985), 105-114. | MR | Zbl

[11] Hopcroft, E. and Ullman, J.D., Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 198. | Zbl

[12] Knuth D.E., 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] Mahler, K., Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366. | JFM | MR

[14] Nikišin, E.M. and Sorokin V.N., Racional'nye approksimacii i ortogonal'nost' (in Russian), Nauka, 1988, 168-175.

[15] Nishioka, K., Shiokawa, I. and Tamura, J., Arithmetical properties of certain power series, (1990), to appear in J. Number Theory. | Zbl

[16] Parusnikov, V.I., Algoritm Jacobi-Perrona i sovmestnoe priblizenie funkcij (in Russian), Mat. Sbornik 114 (156) no. 2 (1982), 322-333. | MR | Zbl

[17] Polya G. and Szegö G., Problems and Theorems in Analysis II, Springer-Verlag, 1976. | Zbl

[18] Rauzy, Nombres algébriques et substitutions, Bull. Soc. Math. France 110 (1982), 147-178. | Numdam | MR | Zbl

[19] Shallit, J.O., A generalization of automatic sequences, Theor. Comput. Sci. 61 (1988), 1-16. | MR | Zbl

[20] Sloane, N.J.A., A Handbook of Integer Sequences, Academic Press, 1973. | Zbl

[21] Stolarsky, K.B., Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull. 19 (1976), 473-482. | MR | Zbl

[22] Zeckendorf, E., 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