Functional graphs of rational maps induced by endomorphisms of ordinary elliptic curves over finite fields

In this paper we study the dynamics of rational maps induced by endomorphisms of ordinary elliptic curves defined over finite fields.Comment: 21 pages, Introduction revised, Section 3.2 revised, minor adjustment

Sequences of irreducible polynomials over odd prime fields via elliptic curve endomorphisms

In this paper we present and analyse a construction of irreducible polynomials over odd prime fields via the transforms which take any polynomial $f \in \mathbf{F}_p[x]$ of positive degree $n$ to $\left(\frac{x}{k} \right)^n \cdot f(k(x+x^{-1}))$, for some specific values of the odd prime $p$ and $k \in \mathbf{F}_p$.Comment: 9 pages. Exposition revised. References update

Sequences of irreducible polynomials without prescribed coefficients over odd prime fields

In this paper we construct infinite sequences of monic irreducible polynomials with coefficients in odd prime fields by means of a transformation introduced by Cohen in 1992. We make no assumptions on the coefficients of the first polynomial $f_0$ of the sequence, which belongs to \F_p [x], for some odd prime $p$, and has positive degree $n$. If $p^{2n}-1 = 2^{e_1} \cdot m$ for some odd integer $m$ and non-negative integer $e_1$, then, after an initial segment $f_0, ..., f_s$ with $s \leq e_1$, the degree of the polynomial $f_{i+1}$ is twice the degree of $f_i$ for any $i \geq s$.Comment: 10 pages. Fixed a typo in the reference

Sequences of binary irreducible polynomials

In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial f_0 \in \F_2 [x]. If $f_0$ is of degree $n = 2^l \cdot m$, where $m$ is odd and $l$ is a non-negative integer, after an initial finite sequence of polynomials $f_0, f_1, ..., f_{s}$ with $s \leq l+3$, the degree of $f_{i+1}$ is twice the degree of $f_i$ for any $i \geq s$.Comment: 7 pages, minor adjustment

On the construction of irreducible polynomials over finite fields via prime degree endomorphisms of elliptic curves

In this paper we present an iterative construction of irreducible polynomials over finite fields based upon repeated applications of transforms induced by endomorphisms of odd prime degree of ordinary elliptic curves.Comment: 6 pages; some inaccuracies and mistakes fixed; presentation revised. A revised version of this paper is to appear in "Periodica Mathematica Hungarica