To appear in Monatsh. Math. ON EXPLICIT BOUNDS FOR THE SOLUTIONS OF A CLASS OF PARAMETRIZED THUE EQUATIONS OF ARBITRARY DEGREE
نویسنده
چکیده
In a recent paper [7] the author considered the family of parametrized Thue equations
منابع مشابه
Effective solution of families of Thue equations containing several parameters
F (X,Y ) = m, where F ∈ Z[X,Y ] is an irreducible form of degree n ≥ 3 and m 6= 0 a fixed integer, has only finitely many solutions. However, this proof is non-effective and does not give any bounds for the size of the possible solutions. In 1968, A. Baker could give effective bounds based on his famous theory on linear forms in logarithms of algebraic numbers. In the last decades, this method ...
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is called Thue equation in honour of A. Thue, who proved in 1909 [19] that the number of its solutions in integers is finite. Thue’s result is not effective, but in 1968, A. Baker [1] gave an upper bound for the solutions using his lower bounds for linear forms in logarithms of algebraic numbers. Since then, algorithms for the solution of single Thue equations have been ∗This work was supported...
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