Titlebook: Elliptic Curves; Diophantine Analysis Serge Lang Book 1978 Springer-Verlag Berlin Heidelberg 1978 Algebra.Arithmetic.Curves.Diophantische A

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Defense

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Auxiliary ResultsThis chapter collects various lemmas of elementary algebraic number theory and complex variables, used to make estimates and to solve interpolation problems.

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manifestation

-Adic Additionuadraticity of the additional formula. This takes place in the general framework that a Lie group has an exponential map convergent near the origin, and giving one-parameter analytic subgroups. We want to see what happens when the base field is .-adic. As before, we carry out the theory ad hoc in a

MEEK

Kummer Theory curve defined over the number field . Let .∈... We look into the field .(.), where . is some point such that .,where misa positive integer. Let .. as usual denote the group of points of period . on . We shall first assume that ..?.. We give a computational proof thatA./2..is finite, making explicit

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Integral Points equations [Si 1] he uses a somewhat different principle. He first reduces the existence of integral points on the curve to the existence of solutions of another equation .where .,. are fixed coefficients, and α,α′ are units in a number field. He then selects an integer . ≥ 3, and coset representati

ARC

The Baker—Feldman Theoremnown to Gelfond for two logarithms, but Baker was the first to see how to deal with more than two. Feldman [Fe 4] then obtained an inequality which is especially good with respect to the heights of the coefficients of the relation, using special interpolation polynomials.

Metastasis

Linear Combinations of Elliptic Logarithmsinequality of this type was given by Masser [Mas I]. We shall follow Coates—Lang [CL], giving a stronger one, with a pattern of proof which follows the original Baker arguments more closely, especially in the use of the Kummer theory.

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