Tabulation of cubic function fields via polynomial binary cubic forms
نویسندگان
چکیده
منابع مشابه
Tabulation of cubic function fields via polynomial binary cubic forms
We present a method for tabulating all cubic function fields over Fq(t) whose discriminant D has either odd degree or even degree and the leading coefficient of −3D is a non-square in Fq , up to a given bound B on deg(D). Our method is based on a generalization of Belabas’ method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport an...
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We give a general method for tabulating all cubic function fields over Fq(t) whose discriminant D has odd degree, or even degree such that the leading coefficient of −3D is a non-square in Fq , up to a given bound on |D| = q. The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields. We present numerical data for cubic function fields o...
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A reduction theory is developed for binary forms (homogeneous polynomials) of degrees three and four with integer coefficients. The resulting coefficient bounds simplify and improve on those in the literature, particularly in the case of negative discriminant. Applications include systematic enumeration of cubic number fields, and 2-descent on elliptic curves defined over Q. Remarks are given c...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2012
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2012-02591-9