Geodesic
On Lagrange algorithm for reduced algebraic irrationalities
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2016), pp. 27-39

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper the properties of Lagrange algorithm for expansion of algebraic number are refined. It has been shown that for reduced algebraic irrationalities the quantity of elementary arithmetic operations which needed for the computation of next incomplete quotient does not depend on the value of this incomplete quotient. It is established that beginning with some index all residual fractions for an arbitrary reduced algebraic irrationality are the generalized Pisot numbers. An asymptotic formula for conjugate numbers to residual fractions is obtained. The definition of generalized Pisot numbers differs from the definition of Pisot numbers by absence of the requirement to be integer. 
@article{BASM_2016_2_a2,
     author = {N. M. Dobrovol'skii and I. N. Balaba and I. Yu. Rebrova and N. N. Dobrovol'skii},
     title = {On {Lagrange} algorithm for reduced algebraic irrationalities},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {27--39},
     publisher = {mathdoc},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2016_2_a2/}
}
TY  - JOUR
AU  - N. M. Dobrovol'skii
AU  - I. N. Balaba
AU  - I. Yu. Rebrova
AU  - N. N. Dobrovol'skii
TI  - On Lagrange algorithm for reduced algebraic irrationalities
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2016
SP  - 27
EP  - 39
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2016_2_a2/
LA  - en
ID  - BASM_2016_2_a2
ER  - 
%0 Journal Article
%A N. M. Dobrovol'skii
%A I. N. Balaba
%A I. Yu. Rebrova
%A N. N. Dobrovol'skii
%T On Lagrange algorithm for reduced algebraic irrationalities
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2016
%P 27-39
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2016_2_a2/
%G en
%F BASM_2016_2_a2
N. M. Dobrovol'skii; I. N. Balaba; I. Yu. Rebrova; N. N. Dobrovol'skii. On Lagrange algorithm for reduced algebraic irrationalities. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2016), pp. 27-39. http://geodesic.mathdoc.fr/item/BASM_2016_2_a2/