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Masser, D. W.

A vanishing theorem for power series. (English) Zbl 0481.10034

Invent. Math. 67, 275-296 (1982).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0481.10034

Cited in 2 Reviews
Cited in 16 Documents

MSC:

11J81 Transcendence (general theory)
30B10 Power series (including lacunary series) in one complex variable
32A05 Power series, series of functions of several complex variables

Keywords:

vanishing theorem; power series; difference of monomials; applications to transcendence theory
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Full Text: DOI EuDML

References:

[1] Ax, J.: On Schanuel’s conjectures. Annals of Math.93, 252-268 (1971) · Zbl 0232.10026 · doi:10.2307/1970774
[2] Baker, A.: Linear forms in the logarithms of algebraic numbers II. Mathematika14, 102-107 (1967) · Zbl 0161.05202 · doi:10.1112/S0025579300008068
[3] Chabauty, C.: Sur les équations diophantiennes liées aux unités d’un corps de nombres algébriques fini. Annali di Mat.17, 127-168 (1938) · Zbl 0019.00303 · doi:10.1007/BF02410698
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[8] Loxton, J.H., van der Poorten, A.J.: Arithmetic properties of certain functions in several variables II. J. Australian Math. Soc.24, 393-408 (1977) · Zbl 0339.10027 · doi:10.1017/S1446788700020772
[9] Loxton, J.H., van der Poorten, A.J.: Arithmetic properties of certain functions in several variables III. Bull. Australian Math. Soc.16, 15-47 (1977) · Zbl 0339.10028 · doi:10.1017/S0004972700022978
[10] Loxton, J.H., van der Poorten, A.J.: Transcendence and algebraic independence by a method of Mahler, Chapter 15 of ?Transcendence theory: advances and applications?, Baker, A., Masser, D.W., (eds.) pp. 211-226. London: Academic Press 1977 · Zbl 0378.10020
[11] Loxton, J.H., van der Poorten, A.J.: Algebraic independence properties of the Fredholm series. J. Australian Math. Soc.26, 31-45 (1978) · Zbl 0392.10034 · doi:10.1017/S1446788700011472
[12] Mahler, K.: Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen. Math. Ann.101, 342-366 (1929) · JFM 55.0115.01 · doi:10.1007/BF01454845
[13] Mahler, K.: Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in spezielle Punktfolgen. Math. Ann.103, 573-587 (1930) · JFM 56.0185.03 · doi:10.1007/BF01455711
[14] Mahler, K.: Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen. Math. Z.32, 545-585 (1930) · JFM 56.0186.01 · doi:10.1007/BF01194652
[15] Mahler, K.: Remarks on a paper by W. Schwarz. J. Number Theory1, 512-521 (1969) · Zbl 0184.07602 · doi:10.1016/0022-314X(69)90013-4
[16] Skolem, Th.: Einige Sätze überp-adische Potenzreihen mit Anwendung auf gewisse exponentielle Gleichungen. Math. Ann.111, 399-424 (1935) · Zbl 0012.01305 · doi:10.1007/BF01472228
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