Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Hermite problem for cubic irrationalities   In this paper, the Hermite problem has been approached finding a periodic
representation (by means of periodic rational or integer sequences) for any
cubic irrationality. In other words, the problem of writing cubic irrationals
as a periodic sequence of rational or integer numbers has been solved. In
particular, a periodic multidimensional continued fraction (with pre--period of
length 2 and period of length 3) is proved convergent to a given cubic
irrationality, by using the algebraic properties of cubic irrationalities and
linear recurrent sequences. This multidimensional continued fraction is derived
from a modification of the Jacobi algorithm, which is proved periodic if and
only if the inputs are cubic irrationals. Moreover, this representation
provides simultaneous rational approximations for cubic irrationals.

29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex