Non-vanishing of Rankin-Selberg convolutions for Hilbert modular forms

In this paper, we study the non-vanishing of the central values of the Rankin-Selberg L -function of two adelic Hilbert primitive forms f and g , both of which have varying weight parameter k . We prove that, for sufficiently large k ∈ 2 N n , there are at least N ( k ) log c N ( k ) adelic Hilbert...

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Veröffentlicht in:Mathematische Zeitschrift 2021-02, Vol.297 (1-2), p.81-97
Hauptverfasser: Hamieh, Alia, Tanabe, Naomi
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we study the non-vanishing of the central values of the Rankin-Selberg L -function of two adelic Hilbert primitive forms f and g , both of which have varying weight parameter k . We prove that, for sufficiently large k ∈ 2 N n , there are at least N ( k ) log c N ( k ) adelic Hilbert primitive forms f of weight k for which L ( 1 2 , f ⊗ g ) are nonzero.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-020-02502-y