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


Authors: Alia Hamieh and Naomi Tanabe
Journal: Trans. Amer. Math. Soc. 369 (2017), 8781-8797
MSC (2010): Primary 11F41, 11F67; Secondary 11F30, 11F11
DOI: https://doi.org/10.1090/tran/6932
Published electronically: May 30, 2017
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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 the work of Luo (1999) to the setting of totally real number fields.


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Additional Information

Alia Hamieh
Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, C526 University Hall, 4401 University Drive, Lethbridge, Alberta T1K3M4, Canada
Email: alia.hamieh@uleth.ca

Naomi Tanabe
Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755-3551
Email: naomi.tanabe@dartmouth.edu

DOI: https://doi.org/10.1090/tran/6932
Keywords: Hilbert modular forms, Rankin-Selberg convolution, Petersson trace formula
Received by editor(s): September 30, 2015
Received by editor(s) in revised form: March 3, 2016
Published electronically: May 30, 2017
Additional Notes: The research of both authors was partially supported by Coleman Postdoctoral Fellowships at Queen’s University
The research of the first author was supported by a PIMS Postdoctoral Fellowship at the University of Lethbridge
Article copyright: © Copyright 2017 American Mathematical Society