L-functions for Quadratic Characters and Annihilation of Motivic Cohomology Groups

Abstract

AbstractLet n be a positive even integer, and let F be a totally real number field and L be an abelian Galois extension which is totally real or CM. Fix a finite set S of primes of F containing the infinite primes and all those which ramify in L, and let SL denote the primes of L lying above those in S. Then OSL denotes the ring of SL-integers of L. Suppose that ψ is a quadratic character of the Galois group of L over F. Under the assumption of the motivic Lichtenbaum conjecture, we obtain a nontrivial annihilator of the motivic cohomology group from the lead term of the Taylor series for the S-modified Artin L-function .