Valuations of Somos 4 sequences and canonical local heignts on elliptic curves
Valuations of Somos 4 sequences and canonical local heignts on elliptic curves
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Somos 4 序列的估值和椭圆曲线上的规范局部高度
DOI：
10.1017/s030500411000068x
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Yukihiro Uchida
中科院分区：
文献类型：
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作者：
Takayuki Hibi;Kyoko Kimura;Satoshi Murai;Yukihiro Uchida
Somos 4序列是由4阶双线性递归关系定义的数字序列，并且包括椭圆整除序列作为特殊情况。在本文中，我们描述的Somos 4序列的典型的局部高度的相关椭圆曲线的估值。我们考虑阿基米德和非阿基米德赋值。作为应用，我们研究了Somos 4序列赋值的渐近性，并得到了某些Somos 4序列的完整性的另一个证明.
Somos 4 sequences are sequences of numbers defined by a bilinear recurrence relation of order 4 and include elliptic divisibility sequences as a special case. In this paper, we describe valuations of Somos 4 sequences in terms of canonical local heights on the associated elliptic curves. We consider both Archimedean and non-Archimedean valuations. As applications, we study the asymptotic behaviour of valuations of Somos 4 sequences and obtain another proof of the integrality of certain Somos 4 sequences.