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On a Family of Quartic Thue Inequalities, II

✍ Scribed by Isao Wakabayashi

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
182 KB
Volume
80
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 # N and k(a, b) is a function with positive values, and we give upper bounds for the solutions when a is larger than a certain constant depending on b.

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 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.

On a Partition Theorem of GΓΆllnitz and Q
On a Partition Theorem of GΓΆllnitz and Quartic Transformations
✍ Krishnaswami Alladi πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 336 KB

For i=1, 2, 3, 4, let Q i (n) denote the number of partitions of n into distinct parts i (mod 4). New weighted identities in three free parameters are established connecting Q i (n) with partitions whose parts differ by 4 and such that consecutive members of the arithmetic progression #i (mod 4) can