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

2016/09/23 by Hamieh, Alia, Tanabe, Naomi
#11F41 #11F67 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.07211

Abstract

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\otimesg, (1)/(2)), where f runs through all primitive Hilbert cusp forms of weight k for infinitely many weight vectors k. This work is a generalization of a result of Ganguly, Hoffstein, and Sengupta to the setting of totally real number fields, and it is a weight aspect analogue of the authors recent work.

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