Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect

Hamieh, Alia; Tanabe, Naomi

doi:10.1090/tran/6932

Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect
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by Alia Hamieh and Naomi Tanabe PDF

Trans. Amer. Math. Soc. 369 (2017), 8781-8797 Request permission

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 the work of Luo (1999) to the setting of totally real number fields.

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