On the complexity of p-adic continued fractions of rational number

TL;DR

This paper investigates the complexity of p-adic continued fractions for rational numbers, focusing on calculating the lengths of Browkin and Schneider expansions and providing numerical examples.

Contribution

It introduces methods to compute the lengths of p-adic continued fraction expansions and analyzes their complexity, extending classical results to the p-adic setting.

Findings

Lengths of Browkin and Schneider expansions are explicitly calculated.

Numerical examples illustrate the theoretical results.

The complexity of p-adic continued fractions is characterized.

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 theorem of Lame. We calculate the length of Browkin expansion, and the length of Schneider expansion. Also, some numerical examples have been given.