Reinhard Schertz

Galoismodulstruktur und elliptische funktionen

Abstract Let K be a quadratic imaginary number field, an integral ideal in K and K( ) the ray class field modulo over K. For certain extensions K( )/K( ∗), ∗| , it is shown that the ring of integers in K( ) is a free rank one module over the associated order (1.2) of K( )/K( ∗) in the group ring of Gal(K( )/K( ∗)) on K( ∗). The associated order and generating elements are both constructed by elliptic functions.

Zur expliziten berechnung von ganzheitsbasen in strahlklassenkörpern über einem imaginär-quadratischen zahlkörper

Abstract Let K be an imaginary quadratic number field, K (1) its Hilbert class field, and K (f) the ray class field modulo f over K , where f is an integral ideal in K . Using suitably normalized values of the weierstrass P -function an explicit method is developed to construct a relative integral basis for K (f)/ K (1).

Über die nenner normierter Teilwerte der Weierstraßschen p-Funktion

Abstract Let K be an imaginary quadratic number field, f an integral ideal in K, and K(f) the ray class field modulo f over K. Using values of a suitably normalized Weierstrass p -function a relative integral basis of K( f ) K(1) was constructed in Schertz (J. Reine Angew. Math. 398). In this paper the denominators of these values, which are important for an explicit construction of integral basis, are completely determined.