Existence of Ramanujan primes for GL(3)
Number Theory
2007-05-23 v2 Representation Theory
Abstract
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.
Cite
@article{arxiv.math/0209140,
title = {Existence of Ramanujan primes for GL(3)},
author = {Dinakar Ramakrishnan},
journal= {arXiv preprint arXiv:math/0209140},
year = {2007}
}
Comments
10 pages