On the de Rham and p-adic realizations of the elliptic polylogarithm for CM elliptic curves

@inproceedings{Bannai2007OnTD,
  title={On the de Rham and p-adic realizations of the elliptic polylogarithm for CM elliptic curves},
  author={Kenichi Bannai and Shinichi Kobayashi and Takeshi Tsuji},
  year={2007}
}
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… CONTINUE READING

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