On Quadratic Fields Generated by the Shanks Sequence
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چکیده
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 S-unit equations as well as bounds for character sums to obtain a lower bound on the number of distinct fields among Q( √ u(n)) for n ∈ {M + 1, . . . ,M + N}. Fields of this type include the Shanks fields and their generalizations.
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تاریخ انتشار 2009