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arXiv · 1609.07209

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

Alia Hamieh·Naomi Tanabe
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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.

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Alia Hamieh, Naomi Tanabe. 2016-09-23. Determining Hilbert Modular Forms by Central Values of Rankin-Selberg Convolutions: The Level Aspect. https://arxiv.org/abs/1609.07209

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