Algebraic independence of the values of generalized Mahler functions

Thomas Töpfer

Acta Arithmetica (1995)

  • Volume: 70, Issue: 2, page 161-181
  • ISSN: 0065-1036

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Thomas Töpfer. "Algebraic independence of the values of generalized Mahler functions." Acta Arithmetica 70.2 (1995): 161-181. <http://eudml.org/doc/206744>.

@article{ThomasTöpfer1995,
author = {Thomas Töpfer},
journal = {Acta Arithmetica},
keywords = {generalized Mahler functions; Mahler's method; transcendence measures; measures of algebraic independence},
language = {eng},
number = {2},
pages = {161-181},
title = {Algebraic independence of the values of generalized Mahler functions},
url = {http://eudml.org/doc/206744},
volume = {70},
year = {1995},
}

TY - JOUR
AU - Thomas Töpfer
TI - Algebraic independence of the values of generalized Mahler functions
JO - Acta Arithmetica
PY - 1995
VL - 70
IS - 2
SP - 161
EP - 181
LA - eng
KW - generalized Mahler functions; Mahler's method; transcendence measures; measures of algebraic independence
UR - http://eudml.org/doc/206744
ER -

References

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  1. [B1] P.-G. Becker, Effective measures for algebraic independence of the values of Mahler type functions, Acta Arith. 58 (1991), 239-250. 
  2. [B2] P.-G. Becker, Algebraic independence of the values of certain series by Mahler's method, Monatsh. Math. 114 (1992), 183-198. Zbl0764.11029
  3. [B3] 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
  4. [B4] P.-G. Becker, Transcendence measures for the values of generalized Mahler functions in arbitrary characteristic, Publ. Math. Debrecen, to appear. 
  5. [BB] P.-G. Becker and W. Bergweiler, Transcendency of local conjugacies in complex dynamics and transcendency of their values, Manuscripta Math. 81 (1993), 329-337. Zbl0808.11045
  6. [DS] J. L. Davison and J. E. Shallit, Continued fractions for some alternating series, Monatsh. Math. 111 (1991), 119-126. Zbl0719.11038
  7. [J] E. M. Jabbouri, Sur un critère pour l'indépendance algébrique de P. Philippon, in: Approximations Diophantiennes et Nombres Transcendants, P. Philippon (ed.), W. de Gruyter, Berlin, 1992, 195-202. Zbl0777.11024
  8. [K1] K. K. Kubota, Linear functional equations and algebraic independence, in: Transcendence Theory: Advances and Applications, A. Baker and D. W. Masser (eds.), Academic Press, New York, 1977, 227-229. 
  9. [K2] K. K. Kubota, On the algebraic independence of holomorphic solutions of certain functional equations and their values, Math. Ann. 227 (1977), 9-50. Zbl0359.10030
  10. [L] J. H. Loxton, Automata and transcendence, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge University Press, Cambridge, 1988, 215-228. 
  11. [LP] 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
  12. [M1] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366. Zbl55.0115.01
  13. [M2] K. Mahler, Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen, Math. Ann. 103 (1930), 573-587. Zbl56.0185.03
  14. [M3] K. Mahler, Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen, Math. Z. 32 (1930), 545-585. Zbl56.0186.01
  15. [M4] K. Mahler, Remarks on a paper by W. Schwarz, J. Number Theory 1 (1969), 512-521. 
  16. [Ni1] K. Nishioka, On a problem of Mahler for transcendency of function values, J. Austral. Math. Soc. Ser. A 33 (1982), 386-393. Zbl0502.10018
  17. [Ni2] K. Nishioka, Algebraic independence measures of the values of Mahler functions, J. Reine Angew. Math. 420 (1991), 203-214. Zbl0736.11034
  18. [NT] K. Nishioka and T. Töpfer, Transcendence measures and nonlinear functional equations of Mahler type, Arch. Math. (Basel) 57 (1991), 370-378. Zbl0704.11014
  19. [Ta] J. Tamura, Symmetric continued fractions related to certain series, J. Number Theory 38 (1991), 251-264. Zbl0734.11005
  20. [T1] T. Töpfer, An axiomatization of Nesterenko's method and applications on Mahler functions, J. Number Theory 49 (1994), 1-26. Zbl0813.11043
  21. [T2] T. Töpfer, An axiomatization of Nesterenko's method and applications on Mahler functions II, Compositio Math., to appear. Zbl0813.11043
  22. [T3] T. Töpfer, Zero order estimates for functions satisfying generalized functional equations of Mahler type, Acta Arith., to appear 

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