p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas

Kenichi Bannai, Hidekazu Furusho, Shinichi Kobayashi

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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 OK 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 languageEnglish
Pages (from-to)269-302
Number of pages34
JournalNagoya Mathematical Journal
Volume219
Issue number1
DOIs
Publication statusPublished - 2015

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ASJC Scopus subject areas

  • Mathematics(all)

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