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References
W. L. Baily, Jr., On the theory of θ-functions, the moduli of abelian varieties, and the moduli of curves, Annals of Math. 75 (1962), 342–381.
W. L. Baily, Jr., Automorphic forms with integral Fourier coefficients, Several complex variables I, Lecture notes in Math. Vol. 155, Springer, Berlin-Heidelberg-New York 1970 (pp. 1–8).
A. Baker, The theory of linear forms in logarithms, Transcendence theory; advances and applications, Academic Press, London 1977 (pp.1–27).
D. Bertrand, Galois orbits on abelian varieties and zero estimates, to appear.
P. Cohen, Explicit calculation of some effective constants in transcendence proofs, Ph. D. Thesis, University of Nottingham 1985 (Chapter 3).
E. Freitag, Siegelsche Modulfunktionen, Grundlehren d. math. Wiss., Vol. 254, Springer, Berlin-Heidelberg-New York 1983.
G. Frey, Some aspects of the theory of elliptic curves over number fields, Expositiones Math. 4 (1986), 35–66
J.-I. Igusa, Theta functions, Grundlehren d. math. Wiss., Vol 194, Springer, Berlin-Heidelberg-New York 1972.
S. Lang, Elliptic curves, diophantine analysis, Grundlehren d. math. Wiss., Vol. 231, Springer, Berlin-Heidelberg-New York 1978.
H. Lange and W. Ruppert, Complete systems of addition laws on abelian varieties, Inventiones Math. 79 (1985), 603–610.
R. C. Mason, Diophantine equations over function fields, London Math. Soc. Lecture Notes, Vol. 96, Cambridge 1984.
D. W. Masser, Small values of the quadratic part of the Néron-Tate height, Progress in Math., Vol. 12, Birkhäuser, Boston-Basel-Stuttgart 1981 (pp.213–222).
D. W. Masser, Small values of the quadratic part of the Néron-Tate height on an abelian variety, Compositio Math. 53 (1984), 153–170.
D. W. Masser, Specializations of Mordell-Weil groups, in preparation.
D. W. Masser and G. Wüstholz, Zero estimates on group varieties II, Inventiones Math. 80 (1985), 233–267.
D. Mumford, On the equations defining abelian varieties II, Inventiones Math. 3 (1967), 75–135.
D. Mumford, Abelian varieties, Oxford 1974.
D. Mumford and J. Fogarty, Geometric invariant theory, Ergebnisse Math., Vol. 34, Springer, Berlin-Heidelberg-New York 1982.
J. V. Nesterenko, Bounds for the characteristic function of a prime ideal, Math. USSR Sbornik 51 (1985), 9–32 (Mat. Sbornik 123 (1984), 11–34).
P. Philippon, Lemmes de zéros dans les groupes algébriques commutatifs, to appear in Bull. Soc. Math. France.
P. Philippon and M. Waldschmidt, Formes linéaires de logarithmes sur les groupes algébriques, in preparation.
G. Shimura, Moduli and fibre systems of abelian varieties, Annals of Math. 83 (1966), 294–338.
C. L. Siegel, Moduln Abelscher Funktionen, Ges. Abh. Vol. III, Springer, Berlin-Heidelberg-New York 1966 (pp.373–435) (Nach Akad. Wiss. Göttingen, Math.-phys. Kl. 25 (1960), 365–427).
J. H. Silverman, Heights and the specialization map for families of abelian varieties, J. reine angew. Math. 342 (1983), 197–211.
J. H. Silverman, Lower bounds for height functions, Duke Math. J. 51 (1984), 395–403.
M. F. Singer and J. H. Davenport, Elementary and Liouvillian solutions of linear differential equations, to appear in J. Symbolic Computation.
J. G. Zarhin and J. I. Manin, Height on families of abelian varieties, Math. USSR Sbornik 18 (1972), 169–179 (Mat. Sbornik 89 (1972), 171–181).
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Masser, D.W. (1987). Small values of heights on families of abelian varieties. In: Wüstholz, G. (eds) Diophantine Approximation and Transcendence Theory. Lecture Notes in Mathematics, vol 1290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078706
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DOI: https://doi.org/10.1007/BFb0078706
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