Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect
Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect
In this paper, we 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 level $\mathfrak {q}$ for infinitely many prime ideals $\mathfrak …