Continued fraction algorithms and Lagrange's theorem in ${\mathbb Q}_p$

Asaki Saito, Jun-ichi Tamura, Shin-ichi Yasutomi

Published 2017-01-17Version 1

We present several continued fraction algorithms, each of which gives an eventually periodic expansion for every quadratic element of ${\mathbb Q}_p$ over ${\mathbb Q}$ and gives a finite expansion for every rational number. We also give, for each of our algorithms, the complete characterization of elements having purely periodic expansions.