Non-vanishing of Rankin-Selberg Convolutions for Hilbert Modular Form

2018/06/12 by Alia Hamieh, Hamieh, Alia, Naomi Tanabe +1
Mathematics · #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1806.04749

openalex publication_date 2018/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the non-vanishing of the central values of the Rankin-Selberg L-function of two adèlic Hilbert primitive forms \bf f and \bf g, both of which have varying weight parameter k. We prove that, for sufficiently large k, there are at least \frack(log k)^c adèlic Hilbert primitive forms \bf f of weight k for which L(\frac12, \bf f⊗\bf g) are nonzero.

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