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 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
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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. |
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ISSN: | 0025-5874 1432-1823 |
DOI: | 10.1007/s00209-020-02502-y |