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

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	English
Pages (from-to)	269-302
Number of pages	34
Journal	Nagoya Mathematical Journal
Volume	219
Issue number	1
DOIs	https://doi.org/10.1215/00277630-2891995
Publication status	Published - 2015 Jan 1

ASJC Scopus subject areas

Mathematics(all)

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10.1215/00277630-2891995

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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.",

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AU - Furusho, Hidekazu

AU - Kobayashi, Shinichi

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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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