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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) Lecture Notes in Mathematics, no. 170 (Springer-Verlag, Berlin-Heidelberg-New York)].

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