Enumeration of quartic fields of small discriminant

Buchmann, Johannes; Ford, David; Pohst, Michael

doi:10.1090/S0025-5718-1993-1176706-0

Enumeration of quartic fields of small discriminant
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by Johannes Buchmann, David Ford and Michael Pohst PDF

Math. Comp. 61 (1993), 873-879 Request permission

Abstract:

With the mixed-type case now completed, all algebraic number fields of degree 4 with absolute discriminant $< {10^6}$ have been enumerated. Methods from the totally real and totally complex cases were used without major modification. Isomorphism of fields was determined by a method similar to one of Lenstra. The ${T_2}$ criterion of Pohst was applied to reduce the number of redundant examples.

References

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Über die Existenz unendlich vieler Primzahlen in einigen speziellen arithmetischen Progressionen

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