Divisibility properties of values of partial zeta functions at non-positive integers

We conjecture a new bound on the exact denominators of the values at non-positive integers of imprimitive partial zeta functions associated with an Abelian extension of number fields. At s?=?0, this conjecture is closely connected to a conjecture of David Hayes. We prove the new conjecture assuming that the Coates–Sinnott conjecture holds for the extension.