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We conjecture the existence of special elements in odd degree higheralgebraic K-groups of number fields that are related in a precise way to thevalues at strictly negative integers of the derivatives of Artin L-functions offinite dimensional complex representations. We prove this conjecture in certainimportant cases and also provide other evidence (both theoretical andnumerical) in its support.

On special elements in higher algebraic K-theory and the Lichtenbaum-Gross Conjecture