The number of solutions of decomposable form equations

@inproceedings{Evertse1995TheNO,
  title={The number of solutions of decomposable form equations},
  author={Jan-Hendrik Evertse},
  year={1995}
}
has only finitely many solutions. The Diophantine approximation techniques of Thue and Mahler and improvements by Siegel, Dyson, Roth and Bombieri made it possible to derive good explicit upper bounds for the number of solutions of (1.1). The best such upper bound to date, due to Bombieri [1] is 2× (12r) (Bombieri assumed that F is irreducible and r ≥ 6 which was not essential in his proof). For t = 0, i.e. |F (x, y)| = 1 in x, y ∈ Z, Bombieri and Schmidt [2] derived the upper bound constant×r… CONTINUE READING
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