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

Abstract

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 $\mathfrak{q}$. This result is a generalization of a theorem of Luo to the setting of totally real number fields.

17 pages

References in corpus (1)

• Notes on the arithmetic of Hilbert modular forms