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

Alexander Goncharov
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Abstract

I compute explicitly the regulator map on $K_4(X)$ 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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BibTeXRIS

Alexander Goncharov. 1996-02-02. Deninger's conjecture on $L$-function of elliptic curves at $s=3$. https://arxiv.org/abs/alg-geom/9512016

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