1. CMB Online first
 Nguyen, Khoa Dang

The HermiteJoubert Problem and a Conjecture of BrassilReichstein
show that Hermite's theorem fails for every
integer $n$ of the form $3^{k_1}+3^{k_2}+3^{k_3}$
with integers $k_1\gt k_2\gt k_3\geq 0$. This confirms
a conjecture of Brassil and Reichstein. We also
obtain new results for the relative
HermiteJoubert problem over a finitely generated
field of characteristic $0$.
Keywords:HermiteJoubert problem, BrassilReichstein conjecture, diophantine equation Categories:11D72, 11G05 

2. CMB 2011 (vol 56 pp. 258)
 Chandoul, A.; Jellali, M.; Mkaouar, M.

The Smallest Pisot Element in the Field of Formal Power Series Over a Finite Field
Dufresnoy and Pisot characterized the smallest
Pisot number of degree $n \geq 3$ by giving explicitly its minimal
polynomial. In this paper, we translate Dufresnoy and Pisot's
result to the Laurent series case.
The
aim of this paper is to prove that the minimal polynomial
of the smallest Pisot element (SPE) of degree $n$ in the field of
formal power series over a finite field
is given by $P(Y)=Y^{n}\alpha XY^{n1}\alpha^n,$ where $\alpha$
is the least element of the finite field $\mathbb{F}_{q}\backslash\{0\}$
(as a finite total ordered set). We prove that the sequence of
SPEs of degree $n$ is decreasing and converges to $\alpha X.$
Finally, we show how to obtain explicit continued fraction
expansion of the smallest Pisot element over a finite field.
Keywords:Pisot element, continued fraction, Laurent series, finite fields Categories:11A55, 11D45, 11D72, 11J61, 11J66 
