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

Jun-Ichi Tamura

Acta Arithmetica (1995)

  • Volume: 71, Issue: 4, page 301-329
  • ISSN: 0065-1036

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Jun-Ichi Tamura. "A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension." Acta Arithmetica 71.4 (1995): 301-329. <http://eudml.org/doc/206777>.

@article{Jun1995,
author = {Jun-Ichi Tamura},
journal = {Acta Arithmetica},
keywords = {Jacobi-Perron algorithm; -adic expansion; rational approximation; transcendence},
language = {eng},
number = {4},
pages = {301-329},
title = {A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension},
url = {http://eudml.org/doc/206777},
volume = {71},
year = {1995},
}

TY - JOUR
AU - Jun-Ichi Tamura
TI - A class of transcendental numbers having explicit g-adic and Jacobi-Perron expansions of arbitrary dimension
JO - Acta Arithmetica
PY - 1995
VL - 71
IS - 4
SP - 301
EP - 329
LA - eng
KW - Jacobi-Perron algorithm; -adic expansion; rational approximation; transcendence
UR - http://eudml.org/doc/206777
ER -

References

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  1. [1] W. W. Adams and J. L. Davison, A remarkable class of continued fractions, Proc. Amer. Math. Soc. 65 (1977), 194-198. Zbl0366.10027
  2. [2] L. Bernstein, The Jacobi-Perron Algorithm. Its Theory and Application, Lecture Notes in Math. 207, Springer, 1971. Zbl0213.05201
  3. [3] P. E. Böhmer, Über die Transzendenz gewisser dyadischer Brüche, Math. Ann. 96 (1927), 367-377. Zbl52.0188.02
  4. [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. Zbl0425.10038
  5. [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. 
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  7. [7] P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), 335-400. Zbl37.0283.01
  8. [8] R. Honsberger, Ingenuity in Mathematics, Random House, 1970. 
  9. [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. [10] S. Kakeya, On the limits of the roots of an algebraic equation with positive coefficients, Tôhoku Math. J. 2 (1912), 140-142. Zbl43.0147.03
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  12. [12] E. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality, Nauka, Moscow, 1988, 168-175 (in Russian). 
  13. [13] K. Nishioka, I. Shiokawa and J. Tamura, Arithmetical properties of certain power series, J. Number Theory 42 (1992), 61-87. Zbl0770.11039
  14. [14] V. I. Parusnikov, The Jacobi-Perron algorithm and simultaneous approximation of functions, Mat. Sb. 114 (156) (1982), 322-333 (in Russian). Zbl0461.30003
  15. [15] G. Pólya and G. Szegö, Problems and Theorems in Analysis II, Springer, 1976. Zbl0311.00002
  16. [16] A. Salomaa, Jewels of Formal Language Theory, Pitman, 1981. Zbl0487.68063
  17. [17] A. Salomaa, Computation and Automata, Cambridge Univ. Press, 1985. Zbl0565.68046
  18. [18] N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973. Zbl0286.10001
  19. [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. Zbl0763.11029
  20. [20] J. Tamura, A class of transcendental numbers with explicit g-adic expansion and the Jacobi-Perron algorithm, Acta Arith. 61 (1992), 51-67. Zbl0747.11029

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