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- Title
Groups generated by iterations of polynomials over finite fields.
- Authors
Shparlinski, Igor E.
- Abstract
Given a finite field of q elements, we consider a trajectory of the map associated with a polynomial ]. Using bounds of character sums, under some mild condition on f, we show that for an appropriate constant C > 0 no N ⩾ Cq½ distinct consecutive elements of such a trajectory are contained in a small subgroup of , improving the trivial lower bound . Using a different technique, we also obtain a similar result for very small values of N. These results are multiplicative analogues of several recently obtained bounds on the length of intervals containing N distinct consecutive elements of such a trajectory.
- Publication
Proceedings of the Edinburgh Mathematical Society, 2016, Vol 59, Issue 1, p235
- ISSN
0013-0915
- Publication type
Article
- DOI
10.1017/S0013091515000097