Dokchitser, Tim; de Jeu, Rob; Zagier, Don Numerical verification of Beilinson’s conjecture for \(K_2\) of hyperelliptic curves. (English) Zbl 1186.11037 Compos. Math. 142, No. 2, 339-373 (2006). Summary: We construct families of hyperelliptic curves over \(\mathbb Q\) 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. Cited in 1 ReviewCited in 10 Documents MSC: 11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 19F27 Étale cohomology, higher regulators, zeta and \(L\)-functions (\(K\)-theoretic aspects) 11G55 Polylogarithms and relations with \(K\)-theory 11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields Keywords:K-theory; regulator; L-function; curve; torsion points PDFBibTeX XMLCite \textit{T. Dokchitser} et al., Compos. Math. 142, No. 2, 339--373 (2006; Zbl 1186.11037) Full Text: DOI arXiv