Constructing and counting number fields

Details Constructing and counting number fields Constructing and counting number fields

2003-04-16

arxiv.org/abs/math/0304231v1

Proceedings of the ICM, Beijing 2002, vol. 2, 129--138

Mathematics

Number Theory

Scientific paper

In this paper we give a survey of recent methods for the asymptotic and exact enumeration of number fields with given Galois group of the Galois closure. In particular, the case of fields of degree up to 4 is now almost completely solved, both in theory and in practice. The same methods also allow construction of the corresponding complete tables of number fields with discriminant up to a given bound.

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