### Abstract

Consider an elliptic curve defined over an imaginary quadratic field K with good reduction at the primes above p ≥ 5 and with complex multiplication by the full ring of integers O_{K} of K. In this paper, we construct p-adic analogues of the Eisenstein-Kronecker series for such an elliptic curve as Coleman functions on the elliptic curve. We then prove p-adic analogues of the first and second Kronecker limit formulas by using the distribution relation of the Kronecker theta function.

Original language | English |
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Pages (from-to) | 269-302 |

Number of pages | 34 |

Journal | Nagoya Mathematical Journal |

Volume | 219 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Bannai, K., Furusho, H., & Kobayashi, S. (2015). p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas.

*Nagoya Mathematical Journal*,*219*(1), 269-302. https://doi.org/10.1215/00277630-2891995