Deninger's conjecture on L-function of elliptic curves at s=3

1995/12/25 by A. B. Goncharov, Alexander Goncharov, Goncharov, Alexander
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9512016

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openalex publication_date 1995/12/25 · arxiv created 1996/02/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I compute explicitly the regulator map on K₄(X) for an arbitrary curve X over a number field. Using this and Beilinson's theorem about regulators for modular curves ([B2]) I prove a formula expressing the value of the L-function L(E,s) of a modular elliptic curve E over \Bbb Q at s=3 by the double Eisenstein-Kronecker series.

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