# Enumerating quartic dihedral extensions of $\mathbb{Q}$ with signatures

Henri Cohen^{[1]}

- [1] Université Bordeaux I, Laboratoire A2X, UR 5465 du CNRS, 351 cours de la Libération, 33405 Talence Cedex (France)

Annales de l’institut Fourier (2003)

- Volume: 53, Issue: 2, page 339-377
- ISSN: 0373-0956

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topCohen, Henri. "Enumerating quartic dihedral extensions of ${\mathbb {Q}}$ with signatures." Annales de l’institut Fourier 53.2 (2003): 339-377. <http://eudml.org/doc/116039>.

@article{Cohen2003,

abstract = {In a previous paper, we have given asymptotic formulas for the number of isomorphism
classes of $D_4$-extensions with discriminant up to a given bound, both when the
signature of the extensions is or is not specified. We have also given very efficient
exact formulas for this number when the signature is not specified. The aim of this paper
is to give such exact formulas when the signature is specified. The problem is
complicated by the fact that the ray class characters which appear are not all genus
characters.},

affiliation = {Université Bordeaux I, Laboratoire A2X, UR 5465 du CNRS, 351 cours de la Libération, 33405 Talence Cedex (France)},

author = {Cohen, Henri},

journal = {Annales de l’institut Fourier},

keywords = {discriminant counting; genus character; quartic reciprocity},

language = {eng},

number = {2},

pages = {339-377},

publisher = {Association des Annales de l'Institut Fourier},

title = {Enumerating quartic dihedral extensions of $\{\mathbb \{Q\}\}$ with signatures},

url = {http://eudml.org/doc/116039},

volume = {53},

year = {2003},

}

TY - JOUR

AU - Cohen, Henri

TI - Enumerating quartic dihedral extensions of ${\mathbb {Q}}$ with signatures

JO - Annales de l’institut Fourier

PY - 2003

PB - Association des Annales de l'Institut Fourier

VL - 53

IS - 2

SP - 339

EP - 377

AB - In a previous paper, we have given asymptotic formulas for the number of isomorphism
classes of $D_4$-extensions with discriminant up to a given bound, both when the
signature of the extensions is or is not specified. We have also given very efficient
exact formulas for this number when the signature is not specified. The aim of this paper
is to give such exact formulas when the signature is specified. The problem is
complicated by the fact that the ray class characters which appear are not all genus
characters.

LA - eng

KW - discriminant counting; genus character; quartic reciprocity

UR - http://eudml.org/doc/116039

ER -

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