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Title

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

Authors 1

Affiliations

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

Bibliography

  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.
Acta Arithmetica
1995/71/4
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Pages:
301-329
Main language of publication
English
Received
1992-01-03
Accepted
1994-09-14
Published
1995
Exact and natural sciences