On unramified cyclic extensions of degree l of algebraic number fields of degree l

Unramified Quaternion Extensions of Quadratic Number Fields

The first mathematician who studied quaternion extensions (H8-extensions for short) was Dedekind [6]; he gave Q( √ (2 + √ 2)(3 + √ 6) ) as an example. The question whether given quadratic or biquadratic number fields can be embedded in a quaternion extension was extensively studied by Rosenblüth [32], Reichardt [31], Witt [36], and Damey and Martinet [5]; see Ledet [19] and the surveys [15] and...

On the Distribution of Cyclic Number Fields of Prime Degree

Let N Cp (X) denote the number of C p Galois extensions of Q with absolute discriminant ≤ X. A well-known theorem of Wright [1] implies that when p is prime, we have N Cp (X) = c(p)X 1 p−1 + O(X 1 p) for some positive real c(p). In this paper, we improve this result by reducing the secondary error term to O(X

Elliptic units of cyclic unramified extensions of complex quadratic fields

On 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...

Procyclic Galois Extensions of Algebraic Number Fields

6 1 Iwasawa’s theory of Zp-extensions 9 1.