We show that the central values of the Rankin-Selberg convolutions, {L(f⊗g, s): f ∈ F}, uniquely determine an adelic Hilbert modular form g; here F is a carefully chosen infinite family of adelic Hilbert modular forms. The key ingredient in the proof is an asymptotic formula for a weighted sum of the central values L(f⊗g, 1/2), where g is fixed and f varies in F. We prove our results when the forms in F are varying in (i) the level aspect and (ii) the weight aspect. This is joint work with Naomi Tanabe.