Semitopological semirings and pushdown automata

Continued Fractions for Algebraic Formal Power Series over a Finite Base Field

Let \({\beta}\) be an algebraic power series over a finite field \({\mathbb{F}_{q}}\) such that \({\beta}\) is not Pisot or Salem series. We study the asymptotic behaviour of the function that counts the number of digit changes in the \({\beta}\)-expansion of 1. As a consequence, we get a transcendence criterion in \({\mathbb{F}_{q}(x)}\) .

In the field of formal power series over a finite field, we prove a result which enables us to construct explicit examples of$U_{m}$-numbers by using continued fraction expansions of algebraic formal power series of degree$m>1$.

E-Algebraic Functions over Fields of Positive Characteristic—An Analogue of Differentially Algebraic Functions

Diophantine Approximation and Continued Fraction Expansions of Algebraic Power Series in Positive Characteristic

SALOMAA1. Introiluction and preliminaries.The theory of formal power series in non- commuting variables was initiated around 1960 -apart from some scattered work done earlier in connection with free groups.Such power series are applicable in a number of areas but, in particular, they have turned out to be an indispensable

Nested Artin strong approximation property