The maximal unramified extensions of the imaginary quadratic number fields with class number two are determined explicitly under the Generalized Riemann Hypothesis.
Γ-extensions of imaginary quadratic fields. II
✍ Scribed by Robert Gold
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 210 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0022-314X
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Focusing on a particular case, we will show that one can explicitly determine the quartic fields \(\mathbf{K}\) that have ideal class groups of exponent \(\leqslant 2\), provided that \(\mathbf{K} / \mathbf{Q}\) is not normal, provided that \(\mathbf{K}\) is a quadratic extension of a fixed imaginar
Let E d ðxÞ denote the ''Euler polynomial'' x 2 þ x þ ð1 À dÞ=4 if d 1 ðmod 4Þ and x 2 À d if d 2; 3 ðmod 4Þ. Set OðnÞ ¼ the number of prime factors (counting multiplicity) of the positive integer n. The Ono invariant Ono d of K is defined to be maxfOðE d ðbÞÞ: b ¼ 0; 1; . . . jD d j=4 À 1g except w