Algebraic independence by Mahler’s method and S -unit equations

Kumiko Nishioka

Compositio Mathematica (1994)

  • Volume: 92, Issue: 1, page 87-110
  • ISSN: 0010-437X

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Nishioka, Kumiko. "Algebraic independence by Mahler’s method and $S$-unit equations." Compositio Mathematica 92.1 (1994): 87-110. <http://eudml.org/doc/90300>.

@article{Nishioka1994,
author = {Nishioka, Kumiko},
journal = {Compositio Mathematica},
keywords = {values at algebraic points; algebraic independence; Mahler functions; Mahler functions of several variables; -unit equation},
language = {eng},
number = {1},
pages = {87-110},
publisher = {Kluwer Academic Publishers},
title = {Algebraic independence by Mahler’s method and $S$-unit equations},
url = {http://eudml.org/doc/90300},
volume = {92},
year = {1994},
}

TY - JOUR
AU - Nishioka, Kumiko
TI - Algebraic independence by Mahler’s method and $S$-unit equations
JO - Compositio Mathematica
PY - 1994
PB - Kluwer Academic Publishers
VL - 92
IS - 1
SP - 87
EP - 110
LA - eng
KW - values at algebraic points; algebraic independence; Mahler functions; Mahler functions of several variables; -unit equation
UR - http://eudml.org/doc/90300
ER -

References

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  2. [2] P.-G. Becker: Effective measures for algebraic independence of the values of Mahler type functions. To appear in Acta Arith. Zbl0735.11030MR1121085
  3. [3] J.-H. Evertse: On sums of S-units and linear recurrences, Compositio Math.53 (1984)225 -244. Zbl0547.10008MR766298
  4. [4] F.R. Gantmacher: Applications of the Theory of Matrices. New York, Wiley, 1959. Zbl0085.01001
  5. [5] K.K. Kubota: On the algebraic independence of holomorphic solutions of certain functional equations and their values. Math. Ann.227 (1977) 9-50. Zbl0359.10030MR498423
  6. [6] J.H. Loxton and A.J. van der Poorten: Arithmetic properties of certain functions in several variables. J. Number Theory9 (1977) 87-106. Zbl0339.10026MR506054
  7. [7] J.H. Loxton and A.J. van der Poorten: Arithmetic properties of certain functions in several variables. II. J. Austral. Math. Soc. Ser.A24 (1977) 393-408. Zbl0339.10027MR506055
  8. [8] J.H. Loxton and A.J. van der Poorten: A class of hypertranscendental functions. Aequationes Math.16 (1977) 93-106. Zbl0384.10014MR476659
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  10. [10] J.H. Loxton and A.J. van der Poorten: Arithmetic properties of automata; regular sequences. J. reine angew. Math.392 (1988) 57-69. Zbl0656.10033MR965057
  11. [11] K. Mahler: Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen. Math. Ann.101 (1929) 342-366. Zbl55.0115.01MR1512537JFM55.0115.01
  12. [12] K. Mahler: Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen. Math. Ann.103 (1930) 573-587. Zbl56.0185.03MR1512638JFM56.0185.03
  13. [13] K. Mahler: Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen. Math. Z.32 (1930) 545-585. Zbl56.0186.01MR1545184JFM56.0186.01
  14. [14] D.W. Masser: A vanishing theorem for power series. Invent. Math.67 (1982) 275-296. Zbl0481.10034MR665158
  15. [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. Zbl0608.10034MR820402
  16. [16] K. Nishioka: New approach in Mahler's method. J. reine angew. Math.407 (1990) 202-219. Zbl0694.10035MR1048535
  17. [17] K. Nishioka: On an estimate for the orders of zeros of Mahler type functions. Acta Arith.56 (1990) 249-256. Zbl0719.11041MR1083004
  18. [18] K. Nishioka: Algebraic independence measures of the values of Mahler functions. J. reine angew. Math.420 (1991) 203-214. Zbl0736.11034MR1124571
  19. [19] K. Nishioka, Y. Shiokawa and J. Tamura: Arithmetic properties of a certain power series. J. Number Theory42 (1992) 61-87. Zbl0770.11039MR1176421

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