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.References
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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
- MR Author ID: 1006617
- Email: alia.hamieh@uleth.ca
- Naomi Tanabe
- Affiliation: Department of Mathematics, Dartmouth College, 6188 Kemeny Hall, Hanover, New Hampshire 03755-3551
- MR Author ID: 915989
- Email: naomi.tanabe@dartmouth.edu
- 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 Queenโs University
The research of the first author was supported by a PIMS Postdoctoral Fellowship at the University of Lethbridge - © Copyright 2017 American Mathematical Society
- 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
- MathSciNet review: 3710644