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Reduction of Binary Cubic and Quartic Forms

Published online by Cambridge University Press:  01 February 2010

J. E. Cremona
J. E. Cremona
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD

Abstract

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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 the set of rational numbers. Remarks are given concerning the extension of these results to forms defined over number fields.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 2 , 1999 , pp. 62 - 92
Copyright
Copyright © London Mathematical Society 1999

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