Solving superelliptic diophantine equations by Baker's method
Language
en
Article de revue
This item was published in
Compositio Mathematica. 1998, vol. 112, n° 3, p. 273--312
Foundation Compositio Mathematica
English Abstract
We describe a method for complete solution of the superelliptic Diophantine equation ay^p=f(x). The method is based on Baker's theory of linear forms in the logarithms. The characteristic feature of our approach (as compared ...Read more >
We describe a method for complete solution of the superelliptic Diophantine equation ay^p=f(x). The method is based on Baker's theory of linear forms in the logarithms. The characteristic feature of our approach (as compared with the classical method is that we reduce the equation directly to the linear forms in logarithms, without intermediate use of Thue and linear unit equations. We show that the reduction method of Baker and Davenport is applicable for superelliptic equations, and develop a very efficient method for enumerating the solutions below the reduced bound. The method requires computing the algebraic data in number fields of degree pn(n-1)/2 at most; in many cases this number can be reduced. Two examples with p=3 and n=4 are given.Read less <
Keywords
soution of diophantine equations
méthode de Baker
Baker's method
résolution d'équations diophantiennes
Origin
Hal imported