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

Kenichi Bannai; Hidekazu Furusho; Shinichi Kobayashi

doi:10.1215/00277630-2891995

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

Kenichi Bannai
, Hidekazu Furusho
, Shinichi Kobayashi

数理科学科

研究成果: Article › 査読

1 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	269-302
ページ数	34
ジャーナル	Nagoya Mathematical Journal
巻	219
号	1
DOI	https://doi.org/10.1215/00277630-2891995
出版ステータス	Published - 2015

ASJC Scopus subject areas

数学一般

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10.1215/00277630-2891995

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

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