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)Â128) <4 article
On Two-parametric Quartic Families of Diophantine Problems
✍ Scribed by A. Pethö; R.F. Tichy
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 510 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0747-7171
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✦ Synopsis
Two-parametric quartic Thue equations are completely solved for sufficiently large values of the parameters. Exceptional units are computed in related quartic number fields. The method depends heavily on A. Baker's theory of linear forms in logarithms and symbolic computation in MAPLE.
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