  Hoffstein and Hulse defined the shifted convolution series of two cusp forms
by "shifting" the usual Rankin-Selberg convolution L-series by a parameter h.
We use the theory of harmonic Maass forms to study the behavior in h-aspect of
certain values of these series and prove a polynomial bound as h approaches
infinity. Our method relies on a result of Mertens and Ono, who showed that
these values are Fourier coefficients of mixed mock modular forms.
