S. Ugolini

activity

20112020

most citedGraphs associated with the map

x \mapsto x + x^{- 1}

in finite fields of characteristic five

14 citations · 73 across the 17 of their papers we have counts for

collaborators

17 papers

math.NT2020★ 3 cited

On the iterations of the maps $a x^{2^{k}} + b$ and $(a x^{2^{k}} + b)^{- 1}$ over finite fields of characteristic two

Simone Ugolini

The maps $x \mapsto a x^{2^{k}} + b$ defined over finite fields of characteristic two can be related to the duplication map over binary supersingular elliptic curves. Relying upon the s…

math.RA2019

Graded Lie algebras of maximal class of type $n$

Sandro Mattarei, Simone Ugolini

Let $n > 1$ be an integer. The algebras of the title, which we abbreviate as algebras of type $n$ , are infinite-dimensional graded Lie algebras $L = ⨁_{i = 1}^{\infty} L_{i}$ , whic…

math.NT2018

Some notes on the multiplicative order of $α + α^{- 1}$ in finite fields of characteristic two

Simone Ugolini

In this paper we prove some results on the possible multiplicative orders of $α + α^{- 1}$ when $α$ is a non-zero element of a finite field of characteristic 2. The results of the pa…

math.NT2016

On permutation numerical semigroups

Simone Ugolini

In this paper we introduce the notion of $n$ -permutation numerical semigroup. While there are just three $2$ -permutation numerical semigroups, there are infinitely many $n$ -permuta…

math.NT2015

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

Simone Ugolini

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 prim…

math.NT2015★ 7 cited

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

Simone Ugolini

In this paper we study the dynamics of rational maps induced by endomorphisms of ordinary elliptic curves defined over finite fields.

math.NT2015

Multiplicative subsemigroups of the positive integers closed with respect to the number of digits

Simone Ugolini

In this paper we present an alternative approach to a problem dealt with by Rosales et al. In particular, once a base $b$ for the representation of the integers is fixed, we descri…

math.NT2015★ 2 cited

On numerical semigroups closed with respect to the action of affine maps

Simone Ugolini

In this paper we study numerical semigroups containing a given positive integer and closed with respect to the action of an affine map. For such semigroups we find a minimal set of…

math.DS2014

Sequences of irreducible polynomials without prescribed coefficients over finite fields of even characteristic

Simone Ugolini

In this paper we deal with the construction of sequences of irreducible polynomials with coefficients in finite fields of even characteristic. We rely upon a transformation used by…

math.NT2013

A graph-based approach to repeating decimals

Simone Ugolini

In this paper we deal with a classical problem in elementary number theory, namely repeating decimals. We show how the digits of the period of the decimal representation of any fra…

math.NT2013★ 2 cited

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

Simone Ugolini

In this paper we present and analyse a construction of irreducible polynomials over odd prime fields via the transforms which take any polynomial $f \in F_{p} [x]$ of positiv…

math.DS2013★ 9 cited

On the iterations of certain maps $x \mapsto k \cdot (x + x^{- 1})$ over finite fields of odd characteristic

Simone Ugolini

In this paper we describe the dynamics of certain rational maps of the form $k \cdot (x + x^{- 1})$ over finite fields of odd characteristic.

math.NT2012★ 4 cited

Sequences of irreducible polynomials without prescribed coefficients over odd prime fields

Simone Ugolini

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 ma…

math.DS2012★ 6 cited

Sequences of binary irreducible polynomials

Simone Ugolini

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…

math.DS2011★ 14 cited

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

Simone Ugolini

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 five.

math.NT2011★ 12 cited

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

Simone Ugolini

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 t…

math.NT2011★ 14 cited

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

Simone Ugolini

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 three.

On the iterations of the maps ax2k+b and (ax2k+b)−1 over finite fields of characteristic two

Graded Lie algebras of maximal class of type n

Some notes on the multiplicative order of α+α−1 in finite fields of characteristic two

On permutation numerical semigroups

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

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

Multiplicative subsemigroups of the positive integers closed with respect to the number of digits

On numerical semigroups closed with respect to the action of affine maps

Sequences of irreducible polynomials without prescribed coefficients over finite fields of even characteristic

A graph-based approach to repeating decimals

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

On the iterations of certain maps x↦k⋅(x+x−1) over finite fields of odd characteristic

Sequences of irreducible polynomials without prescribed coefficients over odd prime fields

Sequences of binary irreducible polynomials

Graphs associated with the map x↦x+x−1 in finite fields of characteristic five

Graphs associated with the map x↦x+x−1 in finite fields of characteristic two

Graphs associated with the map x↦x+x−1 in finite fields of characteristic three

On the iterations of the maps $a x^{2^{k}} + b$ and $(a x^{2^{k}} + b)^{- 1}$ over finite fields of characteristic two

Graded Lie algebras of maximal class of type $n$

Some notes on the multiplicative order of $α + α^{- 1}$ in finite fields of characteristic two

On the iterations of certain maps $x \mapsto k \cdot (x + x^{- 1})$ over finite fields of odd characteristic

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

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 three