Constructing and tabulating dihedral function fields
نویسندگان
چکیده
منابع مشابه
Constructing and tabulating dihedral function fields
We present algorithms for constructing and tabulating degree-` dihedral extensions of Fq(x), where q ≡ 1 mod 2`. We begin with a Kummertheoretic algorithm for constructing these function fields with prescribed ramification and fixed quadratic resolvent field. This algorithm is based on the proof of our main theorem, which gives an exact count for such fields. We then use this construction metho...
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15 صفحه اولCONSTRUCTION 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...
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ژورنال
عنوان ژورنال: The Open Book Series
سال: 2013
ISSN: 2329-907X,2329-9061
DOI: 10.2140/obs.2013.1.557