arXiv subjects

Alain Lasjaunias

Publications and source records attributed to Alain Lasjaunias.

20 records · Page 2Linked to original sources

arXiv2010

On the continued fraction expansion of the unique root in F(p) of the equation x^4+x^2-Tx-1:12=0 and other related hyperquadratic expansions

In 1985, Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, he came across a particular equation of degree 4 in characteristic p=13. This equation has an analogue for all primes p>=5. There are two patterns for the continued fraction of the solution of this equation, according to the residue of p modulo 3. We describe this pattern in the first case, considering especially p=7 and p=13. in the second case we only give indications.

math.NT↗

arXiv2008

Algebraic continued fractions in F_q((T^{-1})) and recurrent sequences in F_q

There exists a particular subset of algebraic power series over a finite field which, for different reasons, can be compared to the subset of quadratic real numbers. The continued fraction expansion for these elements, called hyperquadratic, can sometimes be made explicit. Here we describe this expansion for a wide family of hyperquadratic power series in odd characteristic. This leads to consider interesting recurrent sequences in the finite base field when it is not a prime field.

math.NT↗