ON TAKAGI'S BASIS IN PRIME 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 ...
متن کاملOn Prime Values of Cyclotomic Polynomials
We present several approaches on finding necessary and sufficient conditions on n so that Φk(x ) is irreducible where Φk is the k-th cyclotomic polynomial.
متن کاملCyclotomic Fields
Cyclotomic fields are an interesting laboratory for algebraic number theory because they are connected to fundamental problems Fermat’s Last Theorem for example and also have relatively simple algebraic properties that makes them an excellent laboratory for results in algebraic number theory. I will assume that you are familiar with basic algebraic number theory. Namely, the unique factorizatio...
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...
متن کاملPrime decomposition in the anti-cyclotomic extension
For an imaginary quadratic number field K and an odd prime number l, the anti-cyclotomic Zl-extension of K is defined. For primes p of K, decomposition laws for p in the anti-cyclotomic extension are given. We show how these laws can be applied to determine if the Hilbert class field (or part of it) of K is Zl-embeddable. For some K and l, we find explicit polynomials whose roots generate the f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Memoirs of the Faculty of Science, Kyushu University. Series A, Mathematics
سال: 1972
ISSN: 1883-2172,0373-6385
DOI: 10.2206/kyushumfs.25.265