Algebraic independence by Mahler’s method and S-unit equations
Nishioka, Kumiko
Compositio Mathematica, Tome 94 (1994), p. 87-110 / Harvested from Numdam
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@article{CM_1994__92_1_87_0,
     author = {Nishioka, Kumiko},
     title = {Algebraic independence by Mahler's method and $S$-unit equations},
     journal = {Compositio Mathematica},
     volume = {94},
     year = {1994},
     pages = {87-110},
     mrnumber = {1275722},
     zbl = {0802.11029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1994__92_1_87_0}
}

Nishioka, Kumiko. Algebraic independence by Mahler’s method and $S$-unit equations. Compositio Mathematica, Tome 94 (1994) pp. 87-110. http://gdmltest.u-ga.fr/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 1133238 | Zbl 0735.11031

[2] P.-G. Becker: Effective measures for algebraic independence of the values of Mahler type functions. To appear in Acta Arith. | MR 1121085 | Zbl 0735.11030

[3] J.-H. Evertse: On sums of S-units and linear recurrences, Compositio Math. 53 (1984)225 -244. | Numdam | MR 766298 | Zbl 0547.10008

[4] F.R. Gantmacher: Applications of the Theory of Matrices. New York, Wiley, 1959. | Zbl 0085.01001

[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 498423 | Zbl 0359.10030

[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 506054 | Zbl 0339.10026

[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 506055 | Zbl 0339.10027

[8] J.H. Loxton and A.J. Van Der Poorten: A class of hypertranscendental functions. Aequationes Math. 16 (1977) 93-106. | MR 476659 | Zbl 0384.10014

[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 510583 | Zbl 0392.10034

[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 965057 | Zbl 0656.10033

[11] K. Mahler: Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen. Math. Ann. 101 (1929) 342-366. | JFM 55.0115.01 | MR 1512537

[12] K. Mahler: Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen. Math. Ann. 103 (1930) 573-587. | JFM 56.0185.03 | MR 1512638

[13] K. Mahler: Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen. Math. Z. 32 (1930) 545-585. | JFM 56.0186.01 | MR 1545184

[14] D.W. Masser: A vanishing theorem for power series. Invent. Math. 67 (1982) 275-296. | MR 665158 | Zbl 0481.10034

[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 820402 | Zbl 0608.10034

[16] K. Nishioka: New approach in Mahler's method. J. reine angew. Math. 407 (1990) 202-219. | MR 1048535 | Zbl 0694.10035

[17] K. Nishioka: On an estimate for the orders of zeros of Mahler type functions. Acta Arith. 56 (1990) 249-256. | MR 1083004 | Zbl 0719.11041

[18] K. Nishioka: Algebraic independence measures of the values of Mahler functions. J. reine angew. Math. 420 (1991) 203-214. | MR 1124571 | Zbl 0736.11034

[19] K. Nishioka, Y. Shiokawa and J. Tamura: Arithmetic properties of a certain power series. J. Number Theory 42 (1992) 61-87. | MR 1176421 | Zbl 0770.11039