Continued fractions in local fields, II

Source abstract

The present paper is a continuation of an earlier work by the author. We propose some new definitions of p p -adic continued fractions. At the end of the paper we give numerical examples illustrating these definitions. It turns out that for every m , m, 1 > m > 5000 , 5 ∤ m 1>m>5000,\ 5\nmid m if m ∈ Q 5 ∖ Q , \sqrt {m}\in \mathbb {Q} _{5}\setminus \mathbb {Q}, then m \sqrt {m} has a periodic continued fraction expansion. The same is not true in Q p \mathbb {Q}_{p} for some larger values of p . p.