TY - JOUR

T1 - p-adic Eisenstein-Kronecker series for CM elliptic curves and the Kronecker limit formulas

AU - Bannai, Kenichi

AU - Furusho, Hidekazu

AU - Kobayashi, Shinichi

N1 - Publisher Copyright:
© 2015 by The Editorial Board of the Nagoya Mathematical Journal.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

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U2 - 10.1215/00277630-2891995

DO - 10.1215/00277630-2891995

M3 - Article

AN - SCOPUS:84945264795

SN - 0027-7630

VL - 219

SP - 269

EP - 302

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

IS - 1

ER -