Ideal arithmetic and infrastructure in purely cubic function fields
نویسندگان
چکیده
منابع مشابه
Ideal Arithmetic and Infrastructure in Purely Cubic Function Fields Ideal Arithmetic and Infrastructure in Purely Cubic Function Fields
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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This paper investigates the arithmetic of fractional ideals of a purely cubic function field and the infrastructure of the principal ideal class when the field has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the field. We go on to compute so-called canonical bases of ideals; such bases are very suitable for computation. We st...
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In this paper, we discuss the properties of curves of the form y3 = f(x) over a given field K of characteristic different from 3. If f(x) satisfies certain properties, then the Jacobian of such a curve is isomorphic to the ideal class group of the maximal order in the corresponding function field. We seek to make this connection concrete and then use it to develop an explicit arithmetic for the...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2001
ISSN: 1246-7405
DOI: 10.5802/jtnb.340