On the Complexity of p-Adic Continued Fractions of Rational Number

Rafik Belhadef^1, and Henri-Alex Esbelin²

¹LMPA, Jijel University, BP 98, Jijel, Algeria

²LIMOS, Clermont Auvergne University, Aubière, France

Cite this paper:
Rafik Belhadef and Henri-Alex Esbelin. On the Complexity of p-Adic Continued Fractions of Rational Number. Turkish Journal of Analysis and Number Theory. 2022; 10(1):4-11. doi: 10.12691/tjant-10-1-2

Abstract

In this paper, we study the complexity of p-adic continued fractions of a rational number, which is the p-adic analogue of the Lame’s theorem. We calculate the length of Browkin expansion, and the length of Schneider expansion. Also, some numerical examples have been given.

Keywords:
rational number p-adic number continued fractions

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