On quadratic fields generated by the Shanks sequence

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

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1 Citation (Scopus)
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Abstract

Let u(n)=f(gn), where g > 1 is integer and f(X)ε 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 ε {M+1,⋯,M+N\}. Fields of this type include the Shanks fields and their generalizations.

Original languageEnglish
Pages (from-to)719-729
Number of pages11
JournalProceedings of the Edinburgh Mathematical Society
Volume52
Issue number3
DOIs
Publication statusPublished - Oct 2009

Bibliographical note

Copyright 2009 Cambridge University Press. Article originally published in Proceedings of the Edinburgh Mathematical Society, Vol. 52 No. 3, pp 719-729. The original article can be found at http://dx.doi.org/10.1017/S001309150700123X

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