A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension

• Autorzy: Jun-Ichi Tamura
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 71
• Numer: 4
• Strony: 301-329

Daty

wydano

1995

otrzymano

1992-01-03

poprawiono

1994-09-14

Twórcy

autor

Jun-Ichi Tamura

• Faculty of General Education, International Junior College, Ekoda 4-15-1 Nakano-ku, Tokyo 165, Japan

Bibliografia

• [1] W. W. Adams and J. L. Davison, A remarkable class of continued fractions, Proc. Amer. Math. Soc. 65 (1977), 194-198.
• [2] L. Bernstein, The Jacobi-Perron Algorithm. Its Theory and Application, Lecture Notes in Math. 207, Springer, 1971.
• [3] P. E. Böhmer, Über die Transzendenz gewisser dyadischer Brüche, Math. Ann. 96 (1927), 367-377.
• [4] P. Bundschuh, Über eine Klasse reeller transzendenter Zahlen mit explizit angebbarer g-adischer und Kettenbruch-Entwicklung, J. Reine Angew. Math. 318 (1980), 110-119.
• [5] L. V. Danilov, Some classes of transcendental numbers, Mat. Zametki 12 (1972), 149-154 (in Russian); English transl.: Math. Notes 12 (1972), 524-527.
• [6] J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc. 63 (1977), 29-32.
• [7] P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400.
• [8] R. Honsberger, Ingenuity in Mathematics, Random House, 1970.
• [9] A. Hurwitz, Über einen Satz des Herrn Kakeya, Tôhoku Math. J. 4 (1913), 89-93; also in: Mathematische Werke von Adolf Hurwitz, Bd. II, Birkhäuser, 1963, 627-631.
• [10] S. Kakeya, On the limits of the roots of an algebraic equation with positive coefficients, Tôhoku Math. J. 2 (1912), 140-142.
• [11] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366.
• [12] E. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality, Nauka, Moscow, 1988, 168-175 (in Russian).
• [13] K. Nishioka, I. Shiokawa and J. Tamura, Arithmetical properties of certain power series, J. Number Theory 42 (1992), 61-87.
• [14] V. I. Parusnikov, The Jacobi-Perron algorithm and simultaneous approximation of functions, Mat. Sb. 114 (156) (1982), 322-333 (in Russian).
• [15] G. Pólya and G. Szegö, Problems and Theorems in Analysis II, Springer, 1976.
• [16] A. Salomaa, Jewels of Formal Language Theory, Pitman, 1981.
• [17] A. Salomaa, Computation and Automata, Cambridge Univ. Press, 1985.
• [18] N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973.
• [19] J. Tamura, Transcendental numbers having explicit g-adic and Jacobi-Perron expansions, in: Séminaire de Théorie des Nombres de Bordeaux 4, 1992, 75-95.
• [20] J. Tamura, A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm, Acta Arith. 61 (1992), 51-67.