Existence of Ramanujan primes for GL(3)

Details Existence of Ramanujan primes for GL(3) Existence of Ramanujan primes for GL(3)

2002-09-12

arxiv.org/abs/math/0209140v2

Mathematics

Number Theory

10 pages

Scientific paper

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.

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