Prime factors of class number of cyclotomic fields
نویسندگان
چکیده
منابع مشابه
Class numbers of real cyclotomic fields of prime conductor
The class numbers h+l of the real cyclotomic fields Q(ζl + ζ −1 l ) are notoriously hard to compute. Indeed, the number h+l is not known for a single prime l ≥ 71. In this paper we present a table of the orders of certain subgroups of the class groups of the real cyclotomic fields Q(ζl + ζ −1 l ) for the primes l < 10, 000. It is quite likely that these subgroups are in fact equal to the class ...
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In this paper, criteria of divisibility of the class number h+ of the real cyclotomic field Q(ζp +ζ−1 p ) of a prime conductor p and of a prime degree l by primes q the order modulo l of which is l−1 2 , are given. A corollary of these criteria is the possibility to make a computational proof that a given q does not divide h+ for any p (conductor) such that both p−1 2 , p−3 4 are primes. Note t...
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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. ...
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Let q be a prime power and let Fq be the nite eld with q elements. For each polynomial Q(T) in FqT ], one could use the Carlitz module to construct an abelian extension of Fq(T), called a Carlitz cyclotomic extension. Carlitz cyclotomic extensions play a fundamental role in the study of abelian extensions of Fq(T), similar to the role played by cyclotomic number elds for abelian extensions of Q...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2008
ISSN: 1246-7405
DOI: 10.5802/jtnb.639