Siegel's theorem and the abc conjecture
Surroca, Andrea
HAL, hal-00122044 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 
@article{hal-00122044,
     author = {Surroca, Andrea},
     title = {Siegel's theorem and the abc conjecture},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00122044}
}

Surroca, Andrea. Siegel's theorem and the abc conjecture. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00122044/