On the equality case of the Ramanujan Conjecture for Hilbert modular forms
2019 ◽
Vol 15
(10)
◽
pp. 2107-2114
Keyword(s):
The generalized Ramanujan Conjecture for cuspidal unitary automorphic representations [Formula: see text] on [Formula: see text] posits that [Formula: see text]. We prove that this inequality is strict if [Formula: see text] is generated by a Hilbert modular form of weight two, with complex multiplication, and [Formula: see text] is a finite place of degree one. Equivalently, the Satake parameters of [Formula: see text] are necessarily distinct. We also give examples where the equality case does occur for places [Formula: see text] of degree two.
2009 ◽
Vol 145
(5)
◽
pp. 1081-1113
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2012 ◽
Vol 153
(3)
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pp. 471-487
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Keyword(s):
1979 ◽
Vol 5
(1)
◽
pp. 157-208
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Keyword(s):
2013 ◽
Vol 149
(12)
◽
pp. 1963-2010
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