Algebraic independence by Mahler’s method and S-unit equations
Compositio Mathematica, Tome 92 (1994) no. 1, pp. 87-110.
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     title = {Algebraic independence by {Mahler{\textquoteright}s} method and $S$-unit equations},
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     year = {1994},
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     zbl = {0802.11029},
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     url = {http://archive.numdam.org/item/CM_1994__92_1_87_0/}
}
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Nishioka, Kumiko. Algebraic independence by Mahler’s method and $S$-unit equations. Compositio Mathematica, Tome 92 (1994) no. 1, pp. 87-110. http://archive.numdam.org/item/CM_1994__92_1_87_0/

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

[2] P.-G. Becker: Effective measures for algebraic independence of the values of Mahler type functions. To appear in Acta Arith. | MR | Zbl

[3] J.-H. Evertse: On sums of S-units and linear recurrences, Compositio Math. 53 (1984)225 -244. | Numdam | MR | Zbl

[4] F.R. Gantmacher: Applications of the Theory of Matrices. New York, Wiley, 1959. | Zbl

[5] K.K. Kubota: On the algebraic independence of holomorphic solutions of certain functional equations and their values. Math. Ann. 227 (1977) 9-50. | MR | Zbl

[6] J.H. Loxton and A.J. Van Der Poorten: Arithmetic properties of certain functions in several variables. J. Number Theory 9 (1977) 87-106. | MR | Zbl

[7] J.H. Loxton and A.J. Van Der Poorten: Arithmetic properties of certain functions in several variables. II. J. Austral. Math. Soc. Ser. A 24 (1977) 393-408. | MR | Zbl

[8] J.H. Loxton and A.J. Van Der Poorten: A class of hypertranscendental functions. Aequationes Math. 16 (1977) 93-106. | MR | Zbl

[9] J.H. Loxton and A.J. Van Der Poorten: Algebraic independence properties of the Fredholm series. J. Austral. Math. Soc. Ser. A 26 (1978) 31-45. | MR | Zbl

[10] J.H. Loxton and A.J. Van Der Poorten: Arithmetic properties of automata; regular sequences. J. reine angew. Math. 392 (1988) 57-69. | MR | Zbl

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

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

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

[14] D.W. Masser: A vanishing theorem for power series. Invent. Math. 67 (1982) 275-296. | MR | Zbl

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

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

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

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

[19] K. Nishioka, Y. Shiokawa and J. Tamura: Arithmetic properties of a certain power series. J. Number Theory 42 (1992) 61-87. | MR | Zbl