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On The Equality Case Of The Ramanujan Conjecture For Hilbert Modular Forms, Liubomir Chiriac
On The Equality Case Of The Ramanujan Conjecture For Hilbert Modular Forms, Liubomir Chiriac
Mathematics and Statistics Faculty Publications and Presentations
The generalized Ramanujan Conjecture for cuspidal unitary automorphic representations π on GL(2) asserts that |av(π)| ≤ 2. We prove that this inequality is strict if π is generated by a CM Hilbert modular form of parallel weight two and v is a finite place of degree one. Equivalently, the Satake parameters of πv are necessarily distinct. We also give examples where the equality case does occur for primes of degree two.