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Real Quartic Fields with Small Discriminant

โœ Scribed by Godwin, H. J.

Book ID
120099678
Publisher
Oxford University Press
Year
1956
Tongue
English
Weight
189 KB
Volume
s1-31
Category
Article
ISSN
0024-6107

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to the memory of professor makoto ishida For quartic fields with a quadratic subfield, explicit lower bounds of the regulators are given in terms of the discriminant. Further, these bounds are shown to be in a sense best possible by constructing infinitely many quartic fields with explicit fundament

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We pose the problem of identifying the set K(G, ฮฉ) of Galois number fields with given Galois group G and root discriminant less than the Serre constant ฮฉ โ‰ˆ 44.7632. We definitively treat the cases G = A 4 , A 5 , A 6 and S 4 , S 5 , S 6 , finding exactly 59, 78, 5 and 527, 192, 13 fields, respective