Geodesic
Effective simultaneous approximation of complex numbers by conjugate algebraic integers
Acta Arithmetica, Tome 63 (1993) no. 4, pp. 325-334.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study effectively the simultaneous approximation of n-1 different complex numbers by conjugate algebraic integers of degree n over ℤ(√-1). This is a refinement of a result of Motzkin [2] (see also [3], p. 50) who has no estimate for the remaining conjugate. If the n-1 different complex numbers lie symmetrically about the real axis, then ℤ(√-1) can be replaced by ℤ. In Section 1 we prove an effective version of a Kronecker approximation theorem; we start with an idea of H. Bohr and E. Landau (see e.g. [4]); later we use an estimate of A. Baker for linear forms with logarithms. This and also Rouché's theorem are then applied in Section 2 to give the result; the required irreducibility is guaranteed by the Schönemann-Eisenstein criterion.
DOI : 10.4064/aa-63-4-325-334

G. Rieger 1

1 
@article{10_4064_aa_63_4_325_334,
     author = {G. Rieger},
     title = {Effective simultaneous approximation of complex numbers by conjugate algebraic integers},
     journal = {Acta Arithmetica},
     pages = {325--334},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {1993},
     doi = {10.4064/aa-63-4-325-334},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa-63-4-325-334/}
}
TY  - JOUR
AU  - G. Rieger
TI  - Effective simultaneous approximation of complex numbers by conjugate algebraic integers
JO  - Acta Arithmetica
PY  - 1993
SP  - 325
EP  - 334
VL  - 63
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa-63-4-325-334/
DO  - 10.4064/aa-63-4-325-334
LA  - en
ID  - 10_4064_aa_63_4_325_334
ER  - 
%0 Journal Article
%A G. Rieger
%T Effective simultaneous approximation of complex numbers by conjugate algebraic integers
%J Acta Arithmetica
%D 1993
%P 325-334
%V 63
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa-63-4-325-334/
%R 10.4064/aa-63-4-325-334
%G en
%F 10_4064_aa_63_4_325_334
G. Rieger. Effective simultaneous approximation of complex numbers by conjugate algebraic integers. Acta Arithmetica, Tome 63 (1993) no. 4, pp. 325-334. doi : 10.4064/aa-63-4-325-334. http://geodesic.mathdoc.fr/articles/10.4064/aa-63-4-325-334/

Cité par Sources :