International Journal of Number Theory
Number theory, Modular forms, Hilbert modular surfaces, Eigenvalues
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.
Locate the Document
Chiriac, L. (2019). On the equality case of the Ramanujan Conjecture for Hilbert modular forms. International Journal of Number Theory, 1-8.