Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curves
Numerical verification of Beilinson's conjecture for K2 of hyperelliptic curves
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DOI：
10.1112/s0010437x05001892
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发表时间：
2004-05
影响因子：
1.8
通讯作者：
T. Dokchitser;Rob de Jeu;D. Zagier
中科院分区：
文献类型：
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作者：
T. Dokchitser;Rob de Jeu;D. Zagier
我们构造了任意亏格为g的超椭圆曲线族，在K2中至少有g个整元.对g = 2，3，4，5的几条曲线，我们也用数值方法验证了关于K ~ 2的Beilinson定理。本文的前几节还对曲线的K ~ 2的Beilinson图作了初步的介绍。
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.