English

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

Number Theory 2017-01-18 v1 Dynamical Systems

Abstract

We present several continued fraction algorithms, each of which gives an eventually periodic expansion for every quadratic element of Qp{\mathbb Q}_p over Q{\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.

Keywords

Cite

@article{arxiv.1701.04615,
  title  = {Continued fraction algorithms and Lagrange's theorem in ${\mathbb Q}_p$},
  author = {Asaki Saito and Jun-ichi Tamura and Shin-ichi Yasutomi},
  journal= {arXiv preprint arXiv:1701.04615},
  year   = {2017}
}
R2 v1 2026-06-22T17:52:00.977Z