Let L be a hypergeometric differential operator underlying a family of h^{2,1}=1 Calabi-Yau threefolds. We describe how an investigation of solutions to inhomogeneous equations of the form L(.)=t^{1/d} leads to a reformulation of (certain cases of) Beilinson’s conjectures for members of the family. This is joint work with Vasily Golyshev.