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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.

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Cite

@article{arxiv.math/0209140,
  title  = {Existence of Ramanujan primes for GL(3)},
  author = {Dinakar Ramakrishnan},
  journal= {arXiv preprint arXiv:math/0209140},
  year   = {2007}
}

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10 pages