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

Alexander Goncharov

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

alg-geom 2008-02-03 v2 Algebraic Geometry

Authors: Alexander Goncharov

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.

Keywords

L-function elliptic curve regulator map K-theory Beilinson theorem

Cite

@article{arxiv.alg-geom/9512016,
  title  = {Deninger's conjecture on $L$-function of elliptic curves at $s=3$},
  author = {Alexander Goncharov},
  journal= {arXiv preprint arXiv:alg-geom/9512016},
  year   = {2008}
}

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