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摘要翻译：
本文利用KroneckerTheta函数给出了椭圆曲线的de Rham和p-adic多对数的显式描述。特别证明了当椭圆曲线在p处有复乘和好约简时，p-adic椭圆多对数的扭转点的特殊化与p-adic Eisenstein-Kronecker数有关，证明了Beilinson和Levin用Eisenstein-Kronecker-Lerch级数表示复椭圆多对数的结果的p-adic类似。即使椭圆曲线在p有超奇异约简，我们的结果也是成立的。
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英文标题：
《On the de Rham and p-adic realizations of the Elliptic Polylogarithm for
CM elliptic curves》
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作者：
Kenichi Bannai, Shinichi Kobayashi and Takeshi Tsuji
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最新提交年份：
2008
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分类信息：
一级分类：Mathematics 数学
二级分类：Number Theory 数论
分类描述：Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数，丢番图方程，解析数论，代数数论，算术几何，伽罗瓦理论
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then the specializations to torsion points of the p-adic elliptic polylogarithm are related to p-adic Eisenstein-Kronecker numbers, proving a p-adic analogue of the result of Beilinson and Levin expressing the complex elliptic polylogarithm in terms of Eisenstein-Kronecker-Lerch series. Our result is valid even if the elliptic curve has supersingular reduction at p.
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PDF链接：
https://arxiv.org/pdf/0711.1701
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