Purely cubic complex function fields with small units
نویسندگان
چکیده
منابع مشابه
Purely Cubic Complex Function Fields With Small Units
We investigate several infinite families of purely cubic complex congruence function fields with small fundamental units. Specifically, we compute the fundamental units of fields K of unit rank 1 and characteristic not equal to 3 where the generator of K over Fq(t) is a cube root of D = (M3 − F )/E3 with E3 dividing M3 − F and F dividing M2. We also characterize all purely cubic complex functio...
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A “function field version” of Voronoi’s algorithm can be used to compute the fundamental unit of a purely cubic complex congruence function field of characteristic at least 5. This is accomplished by generating a sequence of minima in the maximal order of the field. The number of mimima computed is the period of the field. Generally, the period is very large — it is proportional to the regulato...
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This paper investigates the arithmetic of fractional ideals and the infrastructure of the principal ideal class of a purely cubic function eld of unit rank one. We rst describe how irreducible polynomials split into prime ideals in purely cubic function elds of nonzero unit rank. This decomposition behavior is used to compute so-called canonical bases of fractional ideals; such bases are very s...
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The first part of this paper classifies all purely cubic function fields over a finite field of characteristic not equal to 3. In the remainder, we describe a method for computing the fundamental unit and regulator of a purely cubic congruence function field of unit rank 1 and characteristic at least 5. The technique is based on Voronoi’s algorithm for generating a chain of successive minima in...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2000
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-95-4-289-304