Existence of Ramanujan primes for GL(3)

Dinakar Ramakrishnan

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Existence of Ramanujan primes for GL(3)

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arxiv math/0209140 v2 pith:PCBLMMEE submitted 2002-09-12 math.NT math.RT

Existence of Ramanujan primes for GL(3)

Dinakar Ramakrishnan This is my paper

classification math.NT math.RT

keywords infinitenumberprimesramanujanadjointcomponentscuspdegree

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In this Note we show that given any cusp form \pi on GL(3) over the rationals, there exist an infinite number of primes p which are Ramanujan for \pi, i.e., that the local components \pi_p 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 \pi.

Existence of Ramanujan primes for GL(3)

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