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 g is uniquely determined by the central values of the Rankin–Selberg L-functions L(f⊗g,12), where f runs through all primitive Hilbert cusp forms of weight k for infinitely many weight vectors k. This result is a generalization of the work of Ganguly et al. (Math Ann 345:843–857, 2009) to the setting of totally real number fields, and it is a weight aspect analogue of our previous work (Hamieh and Tanabe in Trans Am Math Soc, arXiv:1609.07209, 2016).
Hamieh, Alia and Tanabe, Naomi, "Determining Hilbert modular forms by central values of Rankin–Selberg convolutions: the weight aspect" (2018). Mathematics Faculty Publications. 66.