Double coverings for quadratic extensions and function fields

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...

Zp-Extensions of Imaginary Quadratic Fields

Unramified Alternating Extensions of Quadratic Fields

We exhibit, for each n ≥ 5, infinitely many quadratic number fields admitting unramified degree n extensions with prescribed signature whose normal closures have Galois group An. This generalizes a result of Uchida and Yamamoto, which did not include the ability to restrict the signature, and a result of Yamamura, which was the case n = 5. It is a folk conjecture that for n ≥ 5, all but finitel...

Quadratic extensions of totally real quintic fields

In this work, we establish lists for each signature of tenth degree number fields containing a totally real quintic subfield and of discriminant less than 1013 in absolute value. For each field in the list we give its discriminant, the discriminant of its subfield, a relative polynomial generating the field over one of its subfields, the corresponding polynomial over Q, and the Galois group of ...

Algebraic Gamma Monomials and Double Coverings of Cyclotomic Fields

We investigate the properties of algebraic gamma monomials— that is, algebraic numbers which are expressible as monomials in special values of the classical gamma function. Recently Anderson has constructed a double complex SK, to compute H∗(±,U), where U is the universal ordinary distribution. We use the double complex to deduce explicit formulae for algebraic gamma monomials. We provide simpl...