Class number one problem for normal CM-fields
نویسندگان
چکیده
منابع مشابه
The class number one problem for some non-abelian normal CM-fields of degree 48
We determine all the non-abelian normal CM-fields of degree 24 with class number one, provided that the Galois group of their maximal real subfields is isomorphic to A4, the alternating group of degree 4 and order 12. There are two such fields with Galois group A4 × C2 (see Theorem 14) and at most one with Galois group SL2(F3) (see Theorem 18); if the Generalized Riemann Hypothesis is true, the...
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We will show that the normal CM-fields with relative class number one are of degrees ≤ 216. Moreover, if we assume the Generalized Riemann Hypothesis, then the normal CM-fields with relative class number one are of degrees ≤ 96, and the CM-fields with class number one are of degrees ≤ 104. By many authors all normal CM-fields of degrees ≤ 96 with class number one are known except for the possib...
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Since class numbers of CM number fields of a given degree go to infinity with the absolute values of their discriminants, it is reasonable to ask whether the same conclusion still holds true for the exponents of their ideal class groups. We prove that under the assumption of the Generalized Riemann Hypothesis this is indeed the case. 1991 Mathematics Subject Classification. Primary 11R29, 11R21.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2007
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2006.10.012