Cremona, J. E. (2008) Reduction of binary forms over imaginary quadratic fields. In: 60th British Mathematical Colloquium. University of York, 25-28 Mar 2008., University of York, 25-28 Mar 2008 (Unpublished)

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Abstract

We show how the classical theory of reduction of real binary forms with respect to the action of SL(2;Z) may be extended to a reduction theory for binary forms with complex coe�cients under the action of certain discrete groups. In particular, we give some explicit results concerning the reduction of binary cubics and quartics with coe�cients in the ring of integers of an imaginary quadratic �eld of class number one (such as Z[i]), and mention applications to the enumeration of cubic �elds and two-descent on elliptic curves.

Item Type:	Conference Item (Paper)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Official Date:	27 March 2008
Dates:	Date Event 27 March 2008 Completion
Status:	Not Peer Reviewed
Publication Status:	Unpublished
Conference Paper Type:	Paper
Title of Event:	60th British Mathematical Colloquium. University of York, 25-28 Mar 2008.
Type of Event:	Conference
Location of Event:	University of York
Date(s) of Event:	25-28 Mar 2008

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