A survey of computational class field theory

Henri Cohen

Journal de théorie des nombres de Bordeaux (1999)

  • Volume: 11, Issue: 1, page 1-13
  • ISSN: 1246-7405

Abstract

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We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.

How to cite

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Cohen, Henri. "A survey of computational class field theory." Journal de théorie des nombres de Bordeaux 11.1 (1999): 1-13. <http://eudml.org/doc/248346>.

@article{Cohen1999,
abstract = {We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.},
author = {Cohen, Henri},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {class field theory; complex multiplication; Hilbert's class field; Ray class field theory},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Université Bordeaux I},
title = {A survey of computational class field theory},
url = {http://eudml.org/doc/248346},
volume = {11},
year = {1999},
}

TY - JOUR
AU - Cohen, Henri
TI - A survey of computational class field theory
JO - Journal de théorie des nombres de Bordeaux
PY - 1999
PB - Université Bordeaux I
VL - 11
IS - 1
SP - 1
EP - 13
AB - We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.
LA - eng
KW - class field theory; complex multiplication; Hilbert's class field; Ray class field theory
UR - http://eudml.org/doc/248346
ER -

References

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