no. 3
An axiomatization of Nesterenko's method and applications on Mahler functions II
Compositio Mathematica, Tome 95 (1995) no. 3, pp. 323-342 
@article{CM_1995__95_3_323_0,
     author = {T\"opfer, Thomas},
     title = {An axiomatization of {Nesterenko's} method and applications on {Mahler} functions {II}},
     journal = {Compositio Mathematica},
     pages = {323--342},
     year = {1995},
     publisher = {Kluwer Academic Publishers},
     volume = {95},
     number = {3},
     mrnumber = {1318091},
     zbl = {0839.11028},
     language = {en},
     url = {https://www.numdam.org/item/CM_1995__95_3_323_0/}
}
TY  - JOUR
AU  - Töpfer, Thomas
TI  - An axiomatization of Nesterenko's method and applications on Mahler functions II
JO  - Compositio Mathematica
PY  - 1995
SP  - 323
EP  - 342
VL  - 95
IS  - 3
PB  - Kluwer Academic Publishers
UR  - https://www.numdam.org/item/CM_1995__95_3_323_0/
LA  - en
ID  - CM_1995__95_3_323_0
ER  - 
%0 Journal Article
%A Töpfer, Thomas
%T An axiomatization of Nesterenko's method and applications on Mahler functions II
%J Compositio Mathematica
%D 1995
%P 323-342
%V 95
%N 3
%I Kluwer Academic Publishers
%U https://www.numdam.org/item/CM_1995__95_3_323_0/
%G en
%F CM_1995__95_3_323_0
Töpfer, Thomas. An axiomatization of Nesterenko's method and applications on Mahler functions II. Compositio Mathematica, Tome 95 (1995) no. 3, pp. 323-342. https://www.numdam.org/item/CM_1995__95_3_323_0/

[A] M. Amou: Algebraic independence of the values of certain functions at a transcendental number, Acta Arith. 59 (1991) 71-82. | Zbl | MR

[Be1] P.-G. Becker-Landeck: Transcendence measures by Mahler's transcendence method, Bull. Austral. Math. Soc. 33 (1986) 59-65. | Zbl | MR

[Be2] P.-G. Becker-Landeck: MaBe für Algebraische Unabhängigkeit nach einer Methode von Mahler, Acta Arith. 50 (1988) 279-293. | MR

[Be3] P.-G. Becker: Effective measures for algebraic independence of the values of Mahler type functions, Acta Arith. 58 (1991) 239-250. | Zbl | MR

[Br] W.D. Brownawell: Applications of Cayley-Chow forms, in: H. P. Schlickewei and E. Wirsing (eds) Number Theory, Lect. Notes Math. 1380 (1989) pp. 1-18. | Zbl | MR

[Bu] P. Bundschuh: Einführung in die Zahlentheorie, 2. Auflage, Springer, Berlin (1992). | Zbl | MR

[D] G. Diaz: Grands degrés de transcendance pour des familles d'exponentielles, J. Number Theory 31 (1989) 1-23. | Zbl | MR

[J] E.M. Jabbouri: Sur un critère pour l'indépendance algébrique de P. Philippon, in: P. Philippon (ed.) Approximations Diophantiennes et Nombres Transcendants. W. de Gruyter, Berlin (1992) pp. 195-202. | Zbl | MR

[K] K.K. Kubota: Linear functional equations and algebraic independence, in: A. Baker and D. W. Masser (eds) Transcendence Theory: Advances and Applications. Academic Press, New York (1977) pp. 227-229. | Zbl | MR

[L] J. Loxton: Automata and transcendence, in: A. Baker (ed.) New Advances in Transcendence Theory. Cambridge University Press, Cambridge (1988) pp. 215-228. | Zbl | MR

[LvdP] J. Loxton and A.J. Van Der Poorten: Transcendence and algebraic independence by a method of Mahler, in: A. Baker and D. W. Masser (eds) Transcendence Theory: Advances and Applications. Academic Press, New York (1977) pp. 211-226. | Zbl | MR

[M1] K. Mahler: Arithmetische Eigenschaften der Lôsungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929) 342-366. | MR | JFM

[M2] K. Mahler: Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen, Math. Ann. 103 (1930) 573-587. | MR | JFM

[M3] K. Mahler: Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen, Math. Z. 32 (1930) 545-585. | MR | JFM

[M4] K. Mahler: Remarks on a paper by W. Schwarz, J. Number Theory 1 (1969) 512-521. | Zbl | MR

[Ne1] Y.V. Nesterenko: Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers, Izv. Akad. Nauk SSSR, Ser. Mat. 41 (1977) 253-284; English translation in Math. USSR Izv. 11 (1977) 239-270. | Zbl

[Ne2] Y.V. Nesterenko: Estimates for the characteristic function of a prime ideal, Mat. Sb. 123(165) (1984) 11-34; English translation in Math. USSR Sb. 51 (1985) 9-32. | Zbl | MR

[Ne3] Y.V. Nesterenko: On algebraic independence of algebraic powers of algebraic numbers, Mat. Sb. 123(165) (1984) 435-459; English translation in Math. USSR Sb. 51 (1985) 429-454. | Zbl | MR

[Ne4] Y.V. Nesterenko: On a measure of the algebraic independence of the values of certain functions, Mat. Sb. 128(170) (1985) 545-568; English translation in Math. USSR Sb. 56 (1987) 545-567. | Zbl | MR

[Ni1] K. Nishioka: New approach in Mahler's method, J. reine angew. Math. 407 (1990) 202-219. | Zbl | MR

[Ni2] K. Nishioka: On an estimate for the orders of zeros of Mahler type functions, Acta Arith. 56 (1990) 249-256. | Zbl | MR

[Ni3] K. Nishioka: Algebraic independence measures of the values of Mahler functions, J. reine angew. Math. 420 (1991) 203-214. | Zbl | MR

[P1] P. Philippon: Critères pour l'indépendance algébrique, Inst. Hautes Etudes Sci. Publ. Math. 64 (1986) 5-52. | Zbl | MR | Numdam

[P2] P. Philippon: Critères pour l'indépendance algébrique dans les anneaux diophantiens, C.R. Acad. Sci. Paris Sér. I 315 (1992) 511-515. | Zbl | MR

[S] T. Schneider: Einführung in die transzendenten Zahlen, Springer, Berlin (1957). | Zbl | MR

[T1] T. Tôpfer: An axiomatization of Nesterenko's method and applications on Mahler functions, J. Number Theory 49 (1994) 1-26. | Zbl | MR

[T2] T. Töpfer: Untersuchungen zur Algebraischen Unabhängigkeit der Werte Mahlerscher Funktionen, Dissertation, Universität zu Köln (1991).

[W] N.C. Wass: Algebraic independence of the values at algebraic points of a class of functions considered by Mahler, Dissertationes Mathematicae CCCIII (1990). | Zbl | MR