Siegel's theorem and the abc conjecture

Details Siegel's theorem and the abc conjecture Siegel's theorem and the abc conjecture

2004-08-12

arxiv.org/abs/math/0408168v1

Riv. Mat. Univ. Parma (7) 3* (2004), 323--332.

Mathematics

Number Theory

10 pages; to appear in Rivista Matematica dell'Universita' di Parma, Atti del Secondo Convegno Italiano di Teoria dei Numeri

Scientific paper

Following N. Elkies ("ABC implies Mordell") we show that the abc conjecture of Masser-Oesterle implies an effective version of Siegel's theorem about integral points on algebraic curves, i.e. an upper bound for the S-integral points where the dependence on S is explicit. The converse statement is also announced in this note. For both results, the main geometric tool is a theorem of G.V. Belyi.

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