Effective simultaneous approximation of complex numbers by conjugate algebraic integers

G. J. Rieger. "Effective simultaneous approximation of complex numbers by conjugate algebraic integers." Acta Arithmetica 63.4 (1993): 325-334. <http://eudml.org/doc/206524>.

@article{G1993,
abstract = { 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. },
author = {G. J. Rieger},
journal = {Acta Arithmetica},
keywords = {Baker's method; Kronecker theorem},
language = {eng},
number = {4},
pages = {325-334},
title = {Effective simultaneous approximation of complex numbers by conjugate algebraic integers},
url = {http://eudml.org/doc/206524},
volume = {63},
year = {1993},
}

TY - JOUR
AU - G. J. Rieger
TI - Effective simultaneous approximation of complex numbers by conjugate algebraic integers
JO - Acta Arithmetica
PY - 1993
VL - 63
IS - 4
SP - 325
EP - 334
AB - 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.
LA - eng
KW - Baker's method; Kronecker theorem
UR - http://eudml.org/doc/206524
ER -