Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic two

Details Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic two Graphs associated with the map $x \mapsto x+x^{-1}$ in finite fields of characteristic two

2011-07-22

arxiv.org/abs/1107.4565v3

Mathematics

Number Theory

17 pages; one example added; minor adjustments

Scientific paper

In this paper we study the structure of the graphs associated with the
iterations of the map $x \mapsto x+x^{-1}$ 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.

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