2017
DOI: 10.1090/tran/6932
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Determining Hilbert modular forms by central values of Rankin-Selberg convolutions: The level aspect

Abstract: Abstract. In this paper, we prove that a primitive Hilbert cusp form g is uniquely determined by the central values of the Rankin-Selberg L-functions L(f ⊗ g, 1 2 ), where f runs through all primitive Hilbert cusp forms of level q for infinitely many prime ideals q. This result is a generalization of the work of Luo [10] to the setting of totally real number fields.

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Cited by 3 publications
(7 citation statements)
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“…2 ), where f runs through all primitive Hilbert cusp forms of weight k for infinitely many weight vectors k. This result is a generalization of the work of Ganguly, Hoffstein, and Sengupta [3] to the setting of totally real number fields, and it is a weight aspect analogue of the authors own work [6].…”
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confidence: 54%
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“…2 ), where f runs through all primitive Hilbert cusp forms of weight k for infinitely many weight vectors k. This result is a generalization of the work of Ganguly, Hoffstein, and Sengupta [3] to the setting of totally real number fields, and it is a weight aspect analogue of the authors own work [6].…”
mentioning
confidence: 54%
“…
The purpose of this paper is to prove that a primitive Hilbert cusp form g is uniquely determined by the central values of the Rankin-Selberg L-functions L(f ⊗ g, 12 ), where f runs through all primitive Hilbert cusp forms of weight k for infinitely many weight vectors k. This result is a generalization of the work of Ganguly, Hoffstein, and Sengupta [3] to the setting of totally real number fields, and it is a weight aspect analogue of the authors own work [6].
…”
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confidence: 78%
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