Existence of Ramanujan primes for GL(3)

Dinakar Ramakrishnan

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Existence of Ramanujan primes for GL(3)

Dinakar Ramakrishnan

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Abstract

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

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Dinakar Ramakrishnan. 2002-09-26. Existence of Ramanujan primes for GL(3). https://arxiv.org/abs/math/0209140

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