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 …

Classical continued fractions can be introduced in the field of $ p $-adic numbers, where $ p
$-adic continued fractions offer novel perspectives on number representation and …

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 …

We develop a theory of p-adic continued fractions for a quaternion algebra B over Q ramified
at a rational prime p. Many properties holding in the commutative case can be proven also in …

Special kinds of continued fractions have been proved to converge to transcendental real
numbers by means of the celebrated Subspace Theorem. In this paper we study the …

Continued fractions have been generalized over the field of $ p $-adic numbers, where it is
still not known an analogue of the famous Lagrange's Theorem. In general, the periodicity of …

We develop a continued fraction algorithm in finite extensions of $\Q_p $ generalising
certain algorithms in $\Q_p $, and prove the finiteness property for certain small degree …

Let $ K $ be a number field. We show that, up to allowing a finite set of denominators in the
partial quotients, it is possible to define algorithms for $\mathfrak P $-adic continued …

An algebraic integer is said large if all its real or complex embeddings have absolute value
larger than 1. An integral ideal is said large if it admits a large generator. We investigate the …