Existence of Ramanujan primes for GL(3)

Abstract

Let π be a cusp form on GL(n)/Q , i.e., a cuspidal automophic representation of GL(n,A ), where A denotes the adele ring of Q . We will say that a prime p is a Ramanujan prime for π iff the corresponding πp is tempered. The local component πp will necessarily be unramified for almost all p, determined by an unordered n-tuple {α1,p, α2,p, . . . , αn,p} of… (More)

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