Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: the weight aspect

摘要

The purpose of this paper is to prove that a primitive Hilbert cusp form is uniquely determined by the central values of the Rankin-Selberg L-functions , where runs through all primitive Hilbert cusp forms of weight for infinitely many weight vectors . 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, , 2016).