On the standard L-functions of central-simple algebras

In this article, we investigate (up to (Q) over bar) the values of the standard L-function L-Mm(K)(s, Psi) of the algebra M-m(K) over a CM-field K attached to a certain Hecke character Psi of K (defined through a Hecke character psi of the maximal totally real subfield F of K) at s = (k + 2n)/eta(sic); where m less than or equal to k is an element of Z is fixed and depends on the character psi, For All n is an element of Z(+). (C) 2000 Editions scientifiques et medicales Elsevier SAS.