𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Families of Parametrized Thue Equations

✍ Scribed by Clemens Heuberger


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
337 KB
Volume
76
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

✦ 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.


πŸ“œ SIMILAR VOLUMES


Thomas’ Family of Thue Equations Over Im
✍ Clemens Heuberger; Attila PethΕ‘; Robert F Tichy πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 310 KB

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| ≀ 1), if |t| is large enough or if the discriminant of the

On a Family of Quartic Thue Inequalities
✍ Isao Wakabayashi πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 224 KB

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)Γ‚128) <4 article

On a Family of Quartic Thue Inequalities
✍ Isao Wakabayashi πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 182 KB

We give a method of estimation for rational approximation to algebraic numbers of degree 4 of the form -1+(s+-t)Γ‚N+-1+(s&-t)Γ‚N 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

Solving Thue Equations of High Degree
✍ Yuri Bilu; Guillaume Hanrot πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 424 KB

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.