On the l-rank of ideal class groups of certain number fields
نویسندگان
چکیده
منابع مشابه
On the rank of ideal class groups
We review some questions of Shafarevich on the structure of ideal class groups of number elds, and discuss results that provide evidence in support of these questions. The analogy between number elds and algebraic function elds of one variable has long been a fruitful source of inspiration for the development of algebraic number theory. Hilbert's pioneering work in class eld theory, for instanc...
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.
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Following Hasse’s example, various authors have been deriving divisibility properties of minus class numbers of cyclotomic fields by carefully examining the analytic class number formula. In this paper we will show how to generalize these results to CM-fields by using class field theory. Although we will only need some special cases, we have also decided to include a few results on Hasse’s unit...
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We first study some families of maximal real subfields of cyclotomic fields with even class number, and then explore the implications of large plus class numbers of cyclotomic fields. We also discuss capitulation of the minus part and the behaviour of p-class groups in cyclic ramified p-extensions. This is a continuation of [13]; parts I and II are independent, but will be used in part III. 6. ...
متن کاملAn L(1/3) algorithm for ideal class group and regulator computation in certain number fields
We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann’s, who proved a complexity bound of L(1/2, O(1)) when the discriminant tends to infinity with fixed degree. We achieve a subexponential complexity in O(L(1/3, O(1))) when both the discriminant and the degr...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1986
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-47-2-153-166