Continued fractions in the field of 𝑝-adic numbers

Author:

Romeo Giuliano

Abstract

Continued fractions have a long history in number theory, especially in the area of Diophantine approximation. The aim of this expository paper is to survey the main results on the theory of p p -adic continued fractions, i.e., continued fractions defined over the field of p p -adic numbers Q p \mathbb {Q}_p , which in the last years has recorded a considerable increase of interest and research activity. We start from the very first definitions up to the most recent developments and open problems.

Publisher

American Mathematical Society (AMS)

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1. Quaternionic p -adic continued fractions;Communications in Algebra;2024-09-07

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