Determining Hilbert Modular Forms by Central Values of Rankin-Selberg Convolutions: The Weight Aspect

The purpose of this paper is to prove that a primitive Hilbert cusp form \(\mathbf{g}\) is uniquely determined by the central values of the Rankin-Selberg \(L\)-functions \(L(\mathbf{f}\otimes\mathbf{g}, \frac{1}{2})\), where \(\mathbf{f}\) runs through all primitive Hilbert cusp forms of weight \(k\) for infinitely many weight vectors \(k\). This work is a generalization of a result of Ganguly, Hoffstein, and Sengupta to the setting of totally real number fields, and it is a weight aspect analogue of the authors recent work.