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ABSTRACT. Let Q be a positive definite integral quadratic form in ti variables, with the additional property that the adjoint form Q' is also integral.Using the functional equation of the Epstein zeta function, we obtain a symmetric functional equation of the ¿-function of Q with a primitive character to mod q (additive or multiplicative) defined by £io(2(x))C(x)-ï.Re(s) > nl2> where the summation extends over all x e z", x ¥= 0; our result does not depend upon the usual restriction that q be relatively prime to the discriminant of Q, but rather on a much milder restriction.

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