On the values at zero of partial zeta functions for ray classes of a real quadratic field.

Let k be a totally real quadratic field. Let a be an integer of k and m be a positive rational integer. Denote by ( ( (a), ( m), s) be a partial zeta function associated to a ray class containing the principal ideal (a) defined with a conductor (m). We give a formula of the value of (((a),(m),O) by applying the Shintani method to compute special values of partial zeta functions, c.f. [4]. It is an analog ue to the formula of values of a partial zeta function corresponding to a class contained in ( Z / mZ) x of the field ofrational numbers, c.f. Chap. 4, [5]