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

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

1995-12-25

arxiv.org/abs/alg-geom/9512016v2

Mathematics

Algebraic Geometry

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Scientific paper

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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