Masser, D. W.; Wüstholz, G. Zero estimates on group varieties. I. (English) Zbl 0467.10025 Invent. Math. 64, 489-516 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 17 ReviewsCited in 32 Documents MSC: 11J81 Transcendence (general theory) 14L10 Group varieties 30C15 Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) 33E05 Elliptic functions and integrals 11J85 Algebraic independence; Gel’fond’s method 13A15 Ideals and multiplicative ideal theory in commutative rings 32A30 Other generalizations of function theory of one complex variable Keywords:group variety; Neron-Tate height; transcendental numbers; algebraic groups; ideals; degree theory; zero estimates; elliptic functions; abelian varieties; algebraic independence Citations:Zbl 0455.14024; Zbl 0428.10017; Zbl 0436.32005; Zbl 0454.10019 PDF BibTeX XML Cite \textit{D. W. Masser} and \textit{G. Wüstholz}, Invent. Math. 64, 489--516 (1981; Zbl 0467.10025) Full Text: DOI EuDML OpenURL References: [1] Barsotti, I.: A note on abelian varieties. Rend. Circ. Mat. Palermo2, 236-257 (1953) · Zbl 0053.11401 [2] Barsotti, I.: Structure theorems for group varieties. Annali di Mat.38, 77-119 (1955) · Zbl 0068.34301 [3] Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions I. J. Reine Angew. Math.314, 200-216 (1980) · Zbl 0417.10027 [4] Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions II. Duke Math. J.47, 273-295 (1980) · Zbl 0461.10027 [5] Gröbner, W.: Moderne algebraische Geometrie-die idealtheoretischen Grundlagen. Wien und Innsbruck: Springer 1949 · Zbl 0033.12706 [6] Hodge, W.V.D., Pedoe, D.: Methods of algebraic geometry Vol. 2. Cambridge 1952 · Zbl 0048.14502 [7] Kolchin, E.R.: Algebraic groups and algebraic independence. Amer. J. Math.90, 1151-1164 (1968) · Zbl 0169.36701 [8] Masser, D.W.: Small values of the quadratic part of the Néron-Tate height. Progress in Math. Vol 12 (pp. 213-222). Boston-Basel-Stuttgart: Birkhäuser 1981 [9] Masser, D.W.: On polynomials and exponential polynomials in several complex variables. Inventiones Math.63, 81-95 (1981) · Zbl 0454.10019 [10] Masser, D.W., Wüstholz, G.: Algebraic independence properties of values of elliptic functions. To appear in the proceedings of the Exeter Journées Arithmétiques 1980 · Zbl 0577.10034 [11] Mumford, D.: Algebraic geometry I-complex projective varieties. Berlin-Heidelberg-New York: Springer 1976 · Zbl 0356.14002 [12] Nesterenko, J.V.: Estimates for the orders of zeroes of functions of a certain class and their applications in the theory of transcendental numbers (in Russian). Izv. Akad. Nauk. USSR, Ser. Math.41, 253-284 (1977); Math. USSR Izv.11, 239-270 (1977) · Zbl 0354.10026 [13] Seidenberg, A.: Constructions in algebra. Trans. Amer. Math. Soc.197, 273-313 (1974) · Zbl 0356.13007 [14] Waldschmidt, M.: Nombres transcendants et groupes algébriques. Astérisque69-70 (1979) [15] Waldschmidt, M.: Transcendance et exponentielles en plusieurs variables. Inventiones Math.63, 97-127 (1981) · Zbl 0454.10020 [16] Whittaker, E.T., Watson, G.N.: A course of modern analysis. Cambridge 1965 · JFM 45.0433.02 [17] Chudnovsky, G.V.: Degrés de sous-variétés contenant des ?cubes? de groupes algébriques. C.R. Acad. Sci. Paris291A, 117-119 (1980) · Zbl 0497.14023 [18] Hartshorne, R.: Algebraic geometry. New York-Heidelberg-Berlin: Springer 1977 · Zbl 0367.14001 [19] Borel, A.: Linear algebraic groups. New York: W.A. Benjamin 1969 · Zbl 0206.49801 [20] Zariski, O., Samuel, P.: Commutative algebra Vol. II. New York: Springer 1968 · Zbl 0121.27801 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.