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

Bernd Greuel

Acta Arithmetica (2000)

  • Volume: 93, Issue: 1, page 1-20
  • ISSN: 0065-1036

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Bernd Greuel. "Algebraic independence of the values of Mahler functions satisfying implicit functional equations." Acta Arithmetica 93.1 (2000): 1-20. <http://eudml.org/doc/207396>.

@article{BerndGreuel2000,
author = {Bernd Greuel},
journal = {Acta Arithmetica},
keywords = {functional equations; algebraic independence; infinite products},
language = {eng},
number = {1},
pages = {1-20},
title = {Algebraic independence of the values of Mahler functions satisfying implicit functional equations},
url = {http://eudml.org/doc/207396},
volume = {93},
year = {2000},
}

TY - JOUR
AU - Bernd Greuel
TI - Algebraic independence of the values of Mahler functions satisfying implicit functional equations
JO - Acta Arithmetica
PY - 2000
VL - 93
IS - 1
SP - 1
EP - 20
LA - eng
KW - functional equations; algebraic independence; infinite products
UR - http://eudml.org/doc/207396
ER -

References

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  1. [1] P.-G. Becker, Transcendence of the values of functions satisfying generalized Mahler type functional equations, J. Reine Angew. Math. 440 (1993), 111-128. Zbl0770.11037
  2. [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. Zbl0916.11041
  3. [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. Zbl0378.10020
  4. [4] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366. Zbl55.0115.01
  5. [5] K. Mahler, Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen, Math. Z. 32 (1930), 545-585. Zbl56.0186.01
  6. [6] K. Mahler, Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen, Math. Ann. 103 (1930), 573-587. Zbl56.0185.03
  7. [7] K. Mahler, Remarks on a paper by W. Schwarz, J. Number Theory 1 (1969), 512-521. 
  8. [8] K. Nishioka, On a problem of Mahler for transcendency of function values, J. Austral. Math. Soc. Ser. A 33 (1982), 386-393. Zbl0502.10018
  9. [9] K. Nishioka, On a problem of Mahler for transcendency of function values II, Tsukuba J. Math. 7 (1983), 265-279. Zbl0542.10025
  10. [10] K. Nishioka, New approach in Mahler's method, J. Reine Angew. Math. 407 (1990), 202-219. Zbl0694.10035
  11. [11] K. Nishioka, Mahler Functions and Transcendence, Lecture Notes in Math. 1631, Springer, 1996. Zbl0876.11034
  12. [12] T. Schneider, Einführung in die transzendenten Zahlen, Springer, Berlin, 1957. Zbl0077.04703
  13. [13] T. Töpfer, An axiomatization of Nesterenko's method and applications on Mahler functions, J. Number Theory 49 (1994), 1-26. Zbl0813.11043
  14. [14] T. Töpfer, Algebraic independence of the values of generalized Mahler functions, Acta Arith. 70 (1995), 161-181. Zbl0815.11038
  15. [15] T. Töpfer, Simultaneous approximation measures for functions satisfying generalized functional equations of Mahler type, Abh. Math. Sem. Univ. Hamburg 66 (1996), 177-201. Zbl0873.11044
  16. [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. [17] N. C. Wass, Algebraic independence of the values at algebraic points of a class of functions considered by Mahler, Dissertationes Math. 303 (1990). Zbl0707.11050
  18. [18] A. Weil, Foundations of Algebraic Geometry, Colloq. Publ. 29, Amer. Math. Soc., 1962 Zbl0168.18701

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