Multidimensional $p$-adic continued fraction algorithms

TL;DR

This paper introduces a new class of multidimensional $p$-adic continued fraction algorithms, aiming to extend classical theorems like Lagrange's to the $p$-adic setting, with potential implications for number theory.

Contribution

The paper proposes a novel class of multidimensional $p$-adic continued fraction algorithms, including one designed to satisfy a $p$-adic analogue of Lagrange's Theorem.

Findings

A new class of algorithms for multidimensional $p$-adic continued fractions.

An algorithm within this class that is expected to satisfy a $p$-adic Lagrange's Theorem.

Foundations for future proofs of periodicity and convergence in $p$-adic continued fractions.

Abstract

We give a new class of multidimensional $p$-adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that multidimensional $p$-adic version of Lagrange's Theorem holds.