The values at negative integers of the zeta functions of real quadratic fields are rational numbers, and various things are known about their denominators. In comparison, less is known about the values at negative integers of the partial zeta functions associated with narrow ideal classes of real quadratic fields. Recently, Duke gave a conjecture on the upper bound on the denominators of the values at negative integers of the partial zeta function. In this talk, we give a proof of Duke's conjecture using Harder's theorem on Eisenstein classes. This talk is a joint work with Hohto Bekki.