Algebraic independence of the values of generalized Mahler functions

• Autorzy: Thomas Töpfer
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 70
• Numer: 2
• Strony: 161-181

Daty

wydano

1995

otrzymano

1994-03-21

poprawiono

1994-07-15

Twórcy

autor

Thomas Töpfer

• Mathematisches Institut, Universität zu Köln, Weyertal 86-90, D-50931 Köln, Germany

Bibliografia

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• [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.
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• [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