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On the number of solutions of binomial Thue inequalities

✍ Scribed by Rábai, Zs.; Bennett, M.A.; Pink, I.

Book ID
122948889
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
165 KB
Volume
43
Category
Article
ISSN
1571-0653

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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

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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)ÂN+-1+(s&-t)ÂN 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