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Title

Algebraic independence of the values of Mahler functions satisfying implicit functional equations

Authors 1

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  1. Lechenicher Str. 18, D-50937 Köln, Germany

Bibliography

  1. P.-G. Becker, Transcendence of the values of functions satisfying generalized Mahler type functional equations, J. Reine Angew. Math. 440 (1993), 111-128.
  2. V. G. Chirskiĭ, On the algebraic independence of the values of functions satisfying systems of functional equations, Proc. Steklov Inst. Math. 218 (1997), 433-438.
  3. J. H. Loxton and A. J. van der Poorten, Transcendence and algebraic independence by a method of Mahler, in: Transcendence Theory - Advances and Applications, A. Baker and D. W. Masser (eds.), Academic Press, New York, 1977, 211-226.
  4. K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366.
  5. K. Mahler, Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen, Math. Z. 32 (1930), 545-585.
  6. K. Mahler, Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen, Math. Ann. 103 (1930), 573-587.
  7. K. Mahler, Remarks on a paper by W. Schwarz, J. Number Theory 1 (1969), 512-521.
  8. K. Nishioka, On a problem of Mahler for transcendency of function values, J. Austral. Math. Soc. Ser. A 33 (1982), 386-393.
  9. K. Nishioka, On a problem of Mahler for transcendency of function values II, Tsukuba J. Math. 7 (1983), 265-279.
  10. K. Nishioka, New approach in Mahler's method, J. Reine Angew. Math. 407 (1990), 202-219.
  11. K. Nishioka, Mahler Functions and Transcendence, Lecture Notes in Math. 1631, Springer, 1996.
  12. T. Schneider, Einführung in die transzendenten Zahlen, Springer, Berlin, 1957.
  13. T. Töpfer, An axiomatization of Nesterenko's method and applications on Mahler functions, J. Number Theory 49 (1994), 1-26.
  14. T. Töpfer, Algebraic independence of the values of generalized Mahler functions, Acta Arith. 70 (1995), 161-181.
  15. T. Töpfer, Simultaneous approximation measures for functions satisfying generalized functional equations of Mahler type, Abh. Math. Sem. Univ. Hamburg 66 (1996), 177-201.
  16. M. Waldschmidt, Algebraic independence of transcendental numbers: a survey, in: Proceedings of the Fifth Conference of the Canadian Number Theory Association; Monograph on Number Theory, Indian National Science Academy, R. P. Bambah et al. (eds.), to appear; http://www.math.jussieu.fr/ miw, 1998.
  17. N. C. Wass, Algebraic independence of the values at algebraic points of a class of functions considered by Mahler, Dissertationes Math. 303 (1990).
  18. A. Weil, Foundations of Algebraic Geometry, Colloq. Publ. 29, Amer. Math. Soc., 1962
Acta Arithmetica
2000/93/1
Export to PBN, Opens in new tab
Pages:
1-20
Main language of publication
English
Received
1998-10-05
Accepted
1999-03-01
Published
2000
Exact and natural sciences