Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic two
Number Theory
2012-10-09 v3 Dynamical Systems
Abstract
In this paper we study the structure of the graphs associated with the iterations of the map over finite fields of characteristic two. Formulas are given for the length of the cycles and the depth of the trees relying upon the structure of the group of the rational points of Koblitz curves and the congruences of Kloosterman sums modulo powers of 2.
Keywords
Cite
@article{arxiv.1107.4565,
title = {Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic two},
author = {Simone Ugolini},
journal= {arXiv preprint arXiv:1107.4565},
year = {2012}
}
Comments
17 pages; one example added; minor adjustments