A well-known result of Lagrange (1770) characterises quadratic irrationalities as those real
numbers that can be written as periodic continued fractions. Hermite asked in 1848 if there …

We consider expansions of vectors by a general class of multidimensional continued fraction
algorithms. If the expansion is eventually periodic, then we describe the possible structure of …

Abstract In 1848 Ch. Hermite formulated a question on periodic representation of cubic
numbers. In this paper we introduce a new Jacobi–Perron type algorithm that provides …

Multidimensional continued fractions (MCFs) were introduced by Jacobi and Perron to
obtain periodic representations for algebraic irrationals, analogous to the case of simple …

In 1848 Ch.~ Hermite asked if there exists some way to write cubic irrationalities periodically.
A little later in order to approach the problem CGJ~ Jacobi and O.~ Perron generalized the …

Multidimensional continued fractions generalize classical continued fractions with the aim of
providing periodic representations of algebraic irrationalities by means of integer …

Unlike the real case, there are not many studies and general techniques for providing
simultaneous approximations in the field of p-adic numbers\mathbb Q_p Q p. Here, we study …

We discuss the use of matrices for providing sequences of rationals that approximate
algebraic irrationalities. In particular, we study the regular representation of algebraic …

PERIODIC KARYON EXPANSIONS OF ALGEBRAIC UNITS IN MULTIDIMENSIONAL
CONTINUED FRACTIONS - Document - Gale Academic OneFile Use this link to get back to this …

KARYON EXPANSIONS OF PISOT NUMBERS IN MULTIDIMENSIONAL CONTINUED
FRACTIONS Page 1 Journal of Mathematical Sciences, Vol. 225, No. 6, September, 2017 …