References
Barsotti, I.: A note on abelian varieties. Rend. Circ. Mat. Palermo2, 236–257 (1953)
Barsotti, I.: Structure theorems for group varieties. Annali di Mat.38, 77–119 (1955)
Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions I. J. Reine Angew. Math.314, 200–216 (1980)
Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions II. Duke Math. J.47, 273–295 (1980)
Gröbner, W.: Moderne algebraische Geometrie-die idealtheoretischen Grundlagen. Wien und Innsbruck: Springer 1949
Hodge, W.V.D., Pedoe, D.: Methods of algebraic geometry Vol. 2. Cambridge 1952
Kolchin, E.R.: Algebraic groups and algebraic independence. Amer. J. Math.90, 1151–1164 (1968)
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
Masser, D.W.: On polynomials and exponential polynomials in several complex variables. Inventiones Math.63, 81–95 (1981)
Masser, D.W., Wüstholz, G.: Algebraic independence properties of values of elliptic functions. To appear in the proceedings of the Exeter Journées Arithmétiques 1980
Mumford, D.: Algebraic geometry I-complex projective varieties. Berlin-Heidelberg-New York: Springer 1976
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)
Seidenberg, A.: Constructions in algebra. Trans. Amer. Math. Soc.197, 273–313 (1974)
Waldschmidt, M.: Nombres transcendants et groupes algébriques. Astérisque69–70 (1979)
Waldschmidt, M.: Transcendance et exponentielles en plusieurs variables. Inventiones Math.63, 97–127 (1981)
Whittaker, E.T., Watson, G.N.: A course of modern analysis. Cambridge 1965
Chudnovsky, G.V.: Degrés de sous-variétés contenant des ‘cubes’ de groupes algébriques. C.R. Acad. Sci. Paris291A, 117–119 (1980)
Hartshorne, R.: Algebraic geometry. New York-Heidelberg-Berlin: Springer 1977
Borel, A.: Linear algebraic groups. New York: W.A. Benjamin 1969
Zariski, O., Samuel, P.: Commutative algebra Vol. II. New York: Springer 1968
Author information
Authors and Affiliations
Additional information
Dedicated to Professor Th. Schneider on his 70th birthday
Rights and permissions
About this article
Cite this article
Masser, D.W., Wüstholz, G. Zero estimates on group varieties I. Invent Math 64, 489–516 (1981). https://doi.org/10.1007/BF01389279
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01389279