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Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curves

Published online by Cambridge University Press:  13 March 2006

Tim Dokchitser ,
Rob de Jeu  and
Don Zagier
Tim Dokchitser
Affiliation:
Robinson College, Cambridge CB3 9AN, UKt.dokchitser@dpmms.cam.ac.uk
Rob de Jeu
Affiliation:
Department of Mathematical Sciences, University of Durham, Science Laboratories, South Road, Durham DH1 3LE, UKrob.de-jeu@durham.ac.uk
Don Zagier
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany and Collège de France, 3 rue d'Ulm, F-75005 Paris, Francezagier@mpim-bonn.mpg.de
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Abstract

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We construct families of hyperelliptic curves over ${\mathbb Q}$ of arbitrary genus g with (at least) g integral elements in K2. We also verify the Beilinson conjectures about K2 numerically for several curves with g = 2, 3, 4 and 5. The first few sections of the paper also provide an elementary introduction to the Beilinson conjectures for K2 of curves.

Keywords

K-theoryregulatorL-functioncurvetorsion points11G4019E0819F27 (primary)11C0811G30 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 2 , March 2006 , pp. 339 - 373
Copyright
Foundation Compositio Mathematica 2006