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On quadratic fields generated by the Shanks sequence
Published online by Cambridge University Press: 23 September 2009
Abstract
Let u(n)=f(gn), where g > 1 is integer and f(X) ∈ ℤ[X] is non-constant and has no multiple roots. We use the theory of -unit equations as well as bounds for character sums to obtain a lower bound on the number of distinct fields among for n ∈ . Fields of this type include the Shanks fields and their generalizations.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 3 , October 2009 , pp. 719 - 729
- Copyright
- Copyright © Edinburgh Mathematical Society 2009
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