1. CMB 2015 (vol 58 pp. 704)
 Benamar, H.; Chandoul, A.; Mkaouar, M.

On the Continued Fraction Expansion of Fixed Period in Finite Fields
The Chowla conjecture
states that,
if $t$ is any given
positive integer, there are infinitely many prime positive
integers $N$ such that $\operatorname{Per} (\sqrt{N})=t$, where
$\operatorname{Per} (\sqrt{N})$
is the period length of the continued fraction expansion for
$\sqrt{N}$.
C. Friesen proved
that, for any $k\in \mathbb{N}$, there are infinitely many
squarefree integers $N$, where the continued fraction expansion
of $\sqrt{N}$ has a fixed period. In this paper, we describe all
polynomials $Q\in \mathbb{F}_q[X] $ for which the continued fraction
expansion of $\sqrt {Q}$ has a fixed period, also we give a
lower
bound of the number of monic, nonsquares polynomials $Q$ such
that $\deg Q= 2d$ and $ Per \sqrt {Q}=t$.
Keywords:continued fractions, polynomials, formal power series Categories:11A55, 13J05 

2. CMB 2013 (vol 56 pp. 673)
 Ayadi, K.; Hbaib, M.; Mahjoub, F.

Diophantine Approximation for Certain Algebraic Formal Power Series in Positive Characteristic
In this paper, we study rational approximations for certain algebraic power series over a finite field.
We obtain results for irrational elements of strictly positive degree
satisfying an equation of the type
\begin{equation}
\alpha=\displaystyle\frac{A\alpha^{q}+B}{C\alpha^{q}}
\end{equation}
where $(A, B, C)\in
(\mathbb{F}_{q}[X])^{2}\times\mathbb{F}_{q}^{\star}[X]$.
In particular,
we will give, under some conditions on the polynomials $A$, $B$
and $C$, well approximated elements satisfying this equation.
Keywords:diophantine approximation, formal power series, continued fraction Categories:11J61, 11J70 

3. CMB 2006 (vol 49 pp. 256)
 Neelon, Tejinder

A BernsteinWalsh Type Inequality and Applications
A BernsteinWalsh type inequality for $C^{\infty }$ functions of several
variables is derived, which then is applied to obtain analogs and
generalizations of the following classical theorems: (1) BochnakSiciak
theorem: a $C^{\infty }$\ function on $\mathbb{R}^{n}$ that is real
analytic on every line is real analytic; (2) ZornLelong theorem: if a
double power series $F(x,y)$\ converges on a set of lines of positive
capacity then $F(x,y)$\ is convergent; (3) AbhyankarMohSathaye theorem:
the transfinite diameter of the convergence set of a divergent series is
zero.
Keywords:BernsteinWalsh inequality, convergence sets, analytic functions, ultradifferentiable functions, formal power series Categories:32A05, 26E05 
