Hilbert Class Fields of Real Biquadratic Fields
نویسندگان
چکیده
منابع مشابه
Computing the Hilbert class field of real quadratic fields
Using the units appearing in Stark’s conjectures on the values of L-functions at s = 0, we give a complete algorithm for computing an explicit generator of the Hilbert class field of a real quadratic field. Let k be a real quadratic field of discriminant dk, so that k = Q( √ dk), and let ω denote an algebraic integer such that the ring of integers of k is Ok := Z+ ωZ. An important invariant of ...
متن کاملConstruction of Hilbert 2-class Fields
Let F be a number field with odd class number, and suppose that k/F is a quadratic extension. We will deal with the problem of constructing parts of the Hilbert 2-class field towers of such fields k.
متن کاملOn the Computation of Hilbert Class Fields
Let k be an algebraic number eld. We describe a procedure for computing the Hilbert class eld ?(k) of k, i.e. the maximal abelian extension unramiied at all places. In the rst part of the paper we outline the underlying theory and in the second part we present the important algorithms and give several examples.
متن کاملAn explicit treatment of biquadratic function fields
We provide a comprehensive description of biquadratic function fields and their properties, including a characterization of the cyclic and radical cases as well as the constant field. For the cyclic scenario, we provide simple explicit formulas for the ramification index of any rational place, the field discriminant, the genus, and an algorithmically suitable integral basis. In terms of computa...
متن کاملCONSTRUCTION OF HILBERT CLASS FIELDS OF IMAGINARY QUADRATIC FIELDS AND DIHEDRAL EQUATIONS MODULO p
The implementation of the Atkin-Goldwasser-Kilian primality testing algorithm requires the construction of the Hilbert class eld of an imaginary quadratic eld. We describe the computation of a de ning equation for this eld in terms of Weber's class invariants. The polynomial we obtain, noted W(X), has a solvable Galois group. When this group is dihedral, we show how to express the roots of this...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1995
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1010