On the approximation exponent of some hyperquadratic power series. (English) Zbl 1387.11048

Ayadi, Khalil

Bull. Belg. Math. Soc. - Simon Stevin 22, No. 3, 511-520 (2015).

Summary: In this paper, we give the value of the approximation exponent of the hyperquadratic power series satisfying the equation \[ Cx^{r}-Ax^{r-1}-1=0 \] where \(r>2\) is a power of a prime number \(p\), \(A\) and \(C\) are nonzero polynomials over a finite field \(\mathbb{K}\) of characteristic \(p\) and \(\deg A> \deg C\). Further, we exhibit explicitly its continued fraction expansion when \(C\) divides \(A\).

MSC:

11J61

Approximation in non-Archimedean valuations

Keywords:

Diophantine approximation; formal power series; continued fraction