No abstract

Abstract.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. In particular, under some conditions on the polynomials A, B and C, we will give well approximated elements satisfying this equation.

Let Fq be the finite field with q elements and ? Salem series in Fq((X?1)). It is proved in [15] that, in this case, all elements in Fq(X,?) have purely periodic ?-expansion. We characterize the formal power series f in Fq(X,?) with purely periodic ?-expansions by the conjugate vector ~f when ? is a cubic unit. No similar results exist in the real case.