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1995 | 70 | 2 | 161-181
Tytuł artykułu

Algebraic independence of the values of generalized Mahler functions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
70
Numer
2
Strony
161-181
Opis fizyczny
Daty
wydano
1995
otrzymano
1994-03-21
poprawiono
1994-07-15
Twórcy
  • Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931 Köln, Germany
Bibliografia
  • [B1] P.-G. Becker, Effective measures for algebraic independence of the values of Mahler type functions, Acta Arith. 58 (1991), 239-250.
  • [B2] P.-G. Becker, Algebraic independence of the values of certain series by Mahler's method, Monatsh. Math. 114 (1992), 183-198.
  • [B3] P.-G. Becker, Transcendence of the values of functions satisfying generalized Mahler type functional equations, J. Reine Angew. Math. 440 (1993), 111-128.
  • [B4] P.-G. Becker, Transcendence measures for the values of generalized Mahler functions in arbitrary characteristic, Publ. Math. Debrecen, to appear.
  • [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.
  • [DS] J. L. Davison and J. E. Shallit, Continued fractions for some alternating series, Monatsh. Math. 111 (1991), 119-126.
  • [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.
  • [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.
  • [K2] K. K. Kubota, On the algebraic independence of holomorphic solutions of certain functional equations and their values, Math. Ann. 227 (1977), 9-50.
  • [L] J. H. Loxton, Automata and transcendence, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge University Press, Cambridge, 1988, 215-228.
  • [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.
  • [M1] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366.
  • [M2] K. Mahler, Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen, Math. Ann. 103 (1930), 573-587.
  • [M3] K. Mahler, Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen, Math. Z. 32 (1930), 545-585.
  • [M4] K. Mahler, Remarks on a paper by W. Schwarz, J. Number Theory 1 (1969), 512-521.
  • [Ni1] K. Nishioka, On a problem of Mahler for transcendency of function values, J. Austral. Math. Soc. Ser. A 33 (1982), 386-393.
  • [Ni2] K. Nishioka, Algebraic independence measures of the values of Mahler functions, J. Reine Angew. Math. 420 (1991), 203-214.
  • [NT] K. Nishioka and T. Töpfer, Transcendence measures and nonlinear functional equations of Mahler type, Arch. Math. (Basel) 57 (1991), 370-378.
  • [Ta] J. Tamura, Symmetric continued fractions related to certain series, J. Number Theory 38 (1991), 251-264.
  • [T1] T. Töpfer, An axiomatization of Nesterenko's method and applications on Mahler functions, J. Number Theory 49 (1994), 1-26.
  • [T2] T. Töpfer, An axiomatization of Nesterenko's method and applications on Mahler functions II, Compositio Math., to appear.
  • [T3] T. Töpfer, Zero order estimates for functions satisfying generalized functional equations of Mahler type, Acta Arith., to appear
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav70i2p161bwm
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