A relation between automorphic forms on GL(2) and GL(3).

@article{Gelbart1976ARB,
  title={A relation between automorphic forms on GL(2) and GL(3).},
  author={S. Samuel Gelbart and Herv{\'e} Jacquet},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={1976},
  volume={73 10},
  pages={3348-50}
}
Let rho(n) denote the standard n-dimensional representation of GL(n,C) and rho(n) (2) its symmetric square. For each automorphic cuspidal representation pi of GL(2,A) we introduce an Euler product L(s,pi,rho(2) (2)) of degree 3 which we prove is entire. We also prove that there exists an automorphic representation II of GL(3)-"the lift of pi"-with the property that L(s,II,rho(3)) = L(s,pi,rho(2) (2)). Our results confirm conjectures described in a more general context by R. P. Langlands [(1970… CONTINUE READING