Some quartic number fields containing an imaginary quadratic subfield

Stéphane R. Louboutin. "Some quartic number fields containing an imaginary quadratic subfield." Colloquium Mathematicae 122.1 (2011): 139-148. <http://eudml.org/doc/286223>.

@article{StéphaneR2011,
abstract = {Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.},
author = {Stéphane R. Louboutin},
journal = {Colloquium Mathematicae},
keywords = {quartic imaginary fields; quartic polynomials; quadratic fields; discriminant; quartic units.},
language = {eng},
number = {1},
pages = {139-148},
title = {Some quartic number fields containing an imaginary quadratic subfield},
url = {http://eudml.org/doc/286223},
volume = {122},
year = {2011},
}

TY - JOUR
AU - Stéphane R. Louboutin
TI - Some quartic number fields containing an imaginary quadratic subfield
JO - Colloquium Mathematicae
PY - 2011
VL - 122
IS - 1
SP - 139
EP - 148
AB - Let ε be a quartic algebraic unit. We give necessary and sufficient conditions for (i) the quartic number field K = ℚ(ε) to contain an imaginary quadratic subfield, and (ii) for the ring of algebraic integers of K to be equal to ℤ[ε]. We also prove that the class number of such K's goes to infinity effectively with the discriminant of K.
LA - eng
KW - quartic imaginary fields; quartic polynomials; quadratic fields; discriminant; quartic units.
UR - http://eudml.org/doc/286223
ER -