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Thomas’ Family of Thue Equations Over Imaginary Quadratic Fields by Clemens Heuberger; Attila Pethő; Robert F Tichy is a Computer Science article available to read on EtoBox.

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We consider the family of relative Thue equations where the parameter t, the root of unity μ and the solutions x and y are integers in the same imaginary quadratic number field. We prove that there are only trivial solutions (with |x|, |y| ≤ 1), if |t| is large enough or if the discriminant of the quadratic number field is large enough or if Re t = -1/2 (there are a few more solutions in this case which are explicitly listed). In the case Re t = -1/2, an algebraic method is used, in the general case, Baker's method yields the result.

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Author

Clemens Heuberger; Attila Pethő; Robert F Tichy

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0747-7171)

Published

2002

Language

EN

Field

Computer Science (Physical Sciences)