Displaying similar documents to “Lower powers of elliptic units”

Construction of Ray class fields by elliptic units

Reinhard Schertz (1997)

Journal de théorie des nombres de Bordeaux

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From complex multiplication we know that elliptic units are contained in certain ray class fields over a quadratic imaginary number field K , 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 Δ . It is the aim of this paper to show, that in many cases...

A survey of computational class field theory

Henri Cohen (1999)

Journal de théorie des nombres de Bordeaux

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We give a survey of computational class field theory. We first explain how to compute ray class groups and discriminants of the corresponding ray class fields. We then explain the three main methods in use for computing an equation for the class fields themselves: Kummer theory, Stark units and complex multiplication. Using these techniques we can construct many new number fields, including fields of very small root discriminant.

Sign functions of imaginary quadratic fields and applications

Hassan Oukhaba (2005)

Annales de l’institut Fourier

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We propose a definition of sign of imaginary quadratic fields. We give an example of such functions, and use it to define new invariants that are roots of the classical Ramachandra invariants. Also we introduce signed ordinary distributions and compute their signed cohomology by using Anderson's theory of double complex.