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
VL - 219
SP - 269
EP - 302
JO - Nagoya Mathematical Journal
JF - Nagoya Mathematical Journal
SN - 0027-7630
IS - 1
ER -