The class number of cyclotomic function fields
نویسندگان
چکیده
منابع مشابه
Class Numbers of Cyclotomic Function Fields
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...
متن کاملIdeal Class Groups of Cyclotomic Number Fields I
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...
متن کاملIdeal Class Groups of Cyclotomic Number Fields Ii
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 کاملThe Class Number of the Cyclotomic Field.
1. Let g denote any odd prime and h = h(g) the class number of the cyclotomic field R(r), where r is the primitive gth root of unity, R the rational numbers. It is known that we can write: h = h1h2, where hi and h2 (both integers) are the so-called first and second factors of the class number; in fact h2 is the class number of the real field of degree 2 under R(r), namely the field R(D + D-). K...
متن کاملOn divisibility of the class number h+ of the real cyclotomic fields of prime degree l
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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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1981
ISSN: 0022-314X
DOI: 10.1016/0022-314x(81)90021-4