# Algebraic independence of the values of power series generated by linear recurrences

Acta Arithmetica (1996)

- Volume: 74, Issue: 2, page 177-190
- ISSN: 0065-1036

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top## How to cite

topTaka-Aki Tanaka. "Algebraic independence of the values of power series generated by linear recurrences." Acta Arithmetica 74.2 (1996): 177-190. <http://eudml.org/doc/206845>.

@article{Taka1996,

author = {Taka-Aki Tanaka},

journal = {Acta Arithmetica},

keywords = {algebraic independence of the values of power series; linear recurrences},

language = {eng},

number = {2},

pages = {177-190},

title = {Algebraic independence of the values of power series generated by linear recurrences},

url = {http://eudml.org/doc/206845},

volume = {74},

year = {1996},

}

TY - JOUR

AU - Taka-Aki Tanaka

TI - Algebraic independence of the values of power series generated by linear recurrences

JO - Acta Arithmetica

PY - 1996

VL - 74

IS - 2

SP - 177

EP - 190

LA - eng

KW - algebraic independence of the values of power series; linear recurrences

UR - http://eudml.org/doc/206845

ER -

## References

top- [1] J. W. S. Cassels, Local Fields, Cambridge University Press, 1986.
- [2] F. R. Gantmacher, Applications of the Theory of Matrices, Vol. II, Interscience, New York, 1959.
- [3] 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. Zbl0392.10034
- [4] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366. Zbl55.0115.01
- [5] D. W. Masser, A vanishing theorem for power series, Invent. Math. 67 (1982), 275-296. Zbl0481.10034
- [6] K. Nishioka, Conditions for algebraic independence of certain power series of algebraic numbers, Compositio Math. 62 (1987), 53-61. Zbl0615.10042
- [7] K. Nishioka, Algebraic independence of Mahler functions and their values, Tôhoku Math. J., to appear. Zbl0852.11036

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