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On a family of relative quartic Thue inequalities

✍ Scribed by Volker Ziegler

Book ID
104024686
Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
210 KB
Volume
120
Category
Article
ISSN
0022-314X

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✦ Synopsis

We consider the relative Thue inequalities

where the parameters s and t and the solutions X and Y are integers in the same imaginary quadratic number field and t is sufficiently large with respect to s. Furthermore we study the specialization to s = 1:

We find all solutions to these Thue inequalities for |t| > √ 550. Moreover we solve the relative Thue equations

, where the parameter t, the root of unity ΞΌ and the solutions X and Y are integers in the same imaginary quadratic number field. We solve these Thue inequalities respectively equations by using the method of Thue-Siegel.

πŸ“œ SIMILAR VOLUMES

On a Family of Quartic Thue Inequalities
On a Family of Quartic Thue Inequalities I
✍ 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
On a Family of Quartic Thue Inequalities, II
✍ 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

On Families of Parametrized Thue Equatio
On Families of Parametrized Thue Equations
✍ Clemens Heuberger πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 337 KB

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.