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

We conjecture the existence of special elements in odd degree higher algebraic K-groups of number fields that are related in a precise way to the values at strictly negative integers of the derivatives of Artin L-functions of finite dimensional irreducible complex representations. We prove this conjecture for an important family of examples and also provide other evidence (both theoretical and numerical) in its support.