Problèmes de construction en multiplication complexe
Konstruktion von Potenzganzheitsbasen in Strahlklassenkörpern über imaginär-quadratischen Zahlkörpern.
Eine Bemerkung zu einer Arbeit von C. Meyer "Über imaginär-quadratische Körper mit der Klassenzahl 2".
L-Reihen in imaginär-quadratischen Zahlkörpern und ihre Anwendung auf Klassenzahlprobleme bei quadratischen und biquadratischen Zahlkörpern. I.
L-Reihen imaginär-quadratischen Zahlkörpern und ihre Anwendung auf Klassenzahlprobleme bei quadratischen und biquadratischen Zahlkörpern. II.
Die singulären Werte der Weberschen Funktionen f, f1, f2, ...2, ...3.
Die Klassenzahl der Teilkörper abelscher Erweiterungen imaginär-quadratischer Zahlkörper. II.
Über die analytische Klassenzahlformel für reelle abelsche Zahlkörper.
Die Klassenzahl der Teilkörper abelscher Erweiterungen imaginär-quadratischer Zahlkörper. I.
Teilkörper relativ abelscher Erweiterungen imaginär-quadratischer Zahlkörper, deren Klassenzahl durch Primteiler des Körpergrades teilbar ist.
Construction of Ray class fields by elliptic units
From complex multiplication we know that elliptic units are contained in certain ray class fields over a quadratic imaginary number field , and Ramachandra [3] has shown that these ray class fields can even be generated by elliptic units. However the generators constructed by Ramachandra involve very complicated products of high powers of singular values of the Klein form defined below and singular values of the discriminant . It is the aim of this paper to show, that in many cases a generator...
Weber's class invariants revisited
Let be a quadratic imaginary number field of discriminant . For let denote the order of conductor in and its modular invariant which is known to generate the ring class field modulo over . The coefficients of the minimal equation of being quite large Weber considered in [We] the functions defined below and thereby obtained simpler generators of the ring class fields. Later on the singular values of these functions played a crucial role in Heegner’s solution [He] of the class...
Über die Klassenzahl einfach reeller kubischer Zahlkörper
On the generalized principal ideal theorem of complex multiplication
In the -th cyclotomic field a prime number, , the prime is totally ramified and the only ideal above is generated by , with the primitive -th root of unity . Moreover these numbers represent a norm coherent set, i.e. . It is the aim of this article to establish a similar result for the ray class field of conductor over an imaginary quadratic number field where is the power of a prime ideal in . Therefore the exponential function has to be replaced by a suitable elliptic function....
Lower powers of elliptic units
In the previous paper [Sch2] it has been shown that ray class fields over quadratic imaginary number fields can be generated by simple products of singular values of the Klein form defined below. In the present article the second named author has constructed more general products that are contained in ray class fields thereby correcting Theorem 2 of [Sch2]. An algorithm for the computation of the algebraic equations of the numbers in Theorem 1 of this paper has been implemented in a KASH program...
Constructing elliptic curves over finite fields using double eta-quotients
We examine a class of modular functions for whose values generate ring class fields of imaginary quadratic orders. This fact leads to a new algorithm for constructing elliptic curves with complex multiplication. The difficulties arising when the genus of is not zero are overcome by computing certain modular polynomials. Being a product of four -functions, the proposed modular functions can be viewed as a natural generalisation of the functions examined by Weber and usually employed...
Modular curves of composite level
Eine Abschätzung der Klassenzahl gewisser reiner Zahlkörper sechsten Grades.
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