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Imaginary quadratic fields of class number 2

โœ Scribed by Larry Joel Goldstein


Publisher
Elsevier Science
Year
1972
Tongue
English
Weight
607 KB
Volume
4
Category
Article
ISSN
0022-314X

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Let k be an imaginary quadratic number field with C k, 2 , the 2-Sylow subgroup of its ideal class group, isomorphic to Zร‚2Z\_Zร‚2Z\_Zร‚2Z. By the use of various versions of the Kuroda class number formula, we improve significantly upon our previous lower bound for |C k 1 , 2 | , the 2-class number of

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Let N be an imaginary cyclic number field of degree 2n. When n=3 or n=2 m 2, the fields N with class numbers equal to their genus class numbers and the fields N with relative class numbers less than or equal to 4 are completely determined [10,13,26,27]. Now assume that n 5 and n is not a 2-power. In