Duke Mathematical Journal

On the p-adic realization of elliptic polylogarithms for CM-elliptic curves

Kenichi Bannai

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Let E be a CM-elliptic curve over ℚ with good ordinary reduction at a prime p≥5. The purpose of this paper is to construct the p-adic elliptic polylogarithm of E, following the method of A. Beĭlinson and A. Levin. Our main result is that the specializations of this object at torsion points give the special values of the one-variable p-adic L-function of the Grössencharakter associated to E.

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Duke Math. J., Volume 113, Number 2 (2002), 193-236.

First available in Project Euclid: 18 June 2004

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Zentralblatt MATH identifier

Primary: 11G55: Polylogarithms and relations with $K$-theory
Secondary: 11G07: Elliptic curves over local fields [See also 14G20, 14H52] 11G15: Complex multiplication and moduli of abelian varieties [See also 14K22] 14F30: $p$-adic cohomology, crystalline cohomology 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture)


Bannai, Kenichi. On the p -adic realization of elliptic polylogarithms for CM-elliptic curves. Duke Math. J. 113 (2002), no. 2, 193--236. doi:10.1215/S0012-7094-02-11321-0. https://projecteuclid.org/euclid.dmj/1087575250

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