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 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 - 2015 Jan 1 |
ASJC Scopus subject areas
- Mathematics(all)