منابع مشابه
CM-fields with relative class number one
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...
متن کاملFast Computation of Relative Class Numbers of CM-Fields
It was well known that it is easy to compute relative class numbers of abelian CM-fields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, Springer-Verlag, 1982). Here, we provide a technique for computing the relative class number of any CM-field. 1. Statement of the results Proposition 1. Let n ≥ 1...
متن کاملComputation of Relative Class Numbers of Cm-fields
It was well known that it is easy to compute relative class numbers of abelian CM-fields by using generalized Bernoulli numbers (see Theorem 4.17 in Introduction to cyclotomic fields by L. C. Washington, Grad. Texts in Math., vol. 83, Springer-Verlag, 1982). Here, we provide a technique for computing the relative class number of any CM-field. 1. Statement of the results Proposition 1. Let n ≥ 1...
متن کاملExponents of the ideal class groups of CM number fields
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.
متن کاملThe 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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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2005
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-05-01811-9