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
On Thue Inequalities and a Conjecture of Schmidt
β Scribed by J.L. Thunder
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 246 KB
- Volume
- 52
- Category
- Article
- ISSN
- 0022-314X
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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
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