On Families of Parametrized Thue Equations
β Scribed by Clemens Heuberger
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 337 KB
- Volume
- 76
- Category
- Article
- ISSN
- 0022-314X
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β¦ Synopsis
For the family of parametrized Thue equations
where n 4, d i distinct integers satisfying d i {0 or > d i {0, all solutions are determined for sufficiently large values of the integral parameter a using bounds on linear forms in logarithms.
π SIMILAR VOLUMES
We consider the family of relative Thue equations where the parameter t, the root of unity Β΅ and the solutions x and y are integers in the same imaginary quadratic number field. We prove that there are only trivial solutions (with |x|, |y| β€ 1), if |t| is large enough or if the discriminant of the
For integers a 8, we give upper bounds for the solutions of the Thue inequalities |x 4 &a 2 x 2 y 2 + y 4 | k(a), where k(a) is a function with positive values. The method is based on Pade approximations. 1997 Academic Press ak(a), where \*(a)=2+ 2 log(6 -3 a 2 +24) log(27(a 4 &4)Γ128) <4 article
We give a method of estimation for rational approximation to algebraic numbers of degree 4 of the form -1+(s+-t)ΓN+-1+(s&-t)ΓN with s, t # Z and large N # N. Our method is based on Pade approximation. As an application, we consider the Thue inequalities |x 4 &a 2 x 2 y 2 &by 4 | k(a, b), where a, b
We propose a general method for numerical solution of Thue equations, which allows one to solve in reasonable time Thue equations of high degree (provided necessary algebraic number theory data is available). We illustrate our method, solving completely concrete Thue equations of degrees 19 and 33.