Numerical verification of Beilinson's conjecture for K_2 of hyperelliptic curves

Dokchitser, T.; de Jeu, R.; Zagier, D.

Abstract

We construct families of hyperelliptic curves over Q of arbitrary genus g with (at least) g integral elements in K-2. We also verify the Beilinson conjectures about K-2 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 K-2 of curves.

Citation

Dokchitser, T., de Jeu, R., & Zagier, D. (2006). Numerical verification of Beilinson's conjecture for K_2 of hyperelliptic curves. Compositio Mathematica, 142(2), 339-373. https://doi.org/10.1112/s0010437x05001892

• Journal Article Type: Article
• Publication Date: Mar 1, 2006
• Deposit Date: May 23, 2008
• Publicly Available Date: Feb 11, 2010
• Journal: Compositio Mathematica
• Print ISSN: 0010-437X
• Electronic ISSN: 1570-5846
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 142
• Issue: 2
• Pages: 339-373
• DOI: https://doi.org/10.1112/s0010437x05001892
• Keywords: K-theory, Regulator, L-function, Curve, Torsion points.
• Public URL: https://durham-repository.worktribe.com/output/1591409