Existence of Ramanujan primes for GL(3)
Abstract
In this Note we show that given any cusp form π on GL(3) over the rationals, there exist an infinite number of primes p which are Ramanujan for π, i.e., that the local components πp are tempered for an infinite number of p. It turns out that the key structural device which is needed is the degree 8 adjoint L-function of π.
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