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

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

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Authors

T. Dokchitser

R. de Jeu

D. Zagier



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.

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