RANKIN–SELBERG INTEGRALS FOR LOCAL SYMMETRIC SQUARE FACTORS ON G L ( 2 )

Let π be an irreducible admissible (complex) representation of G L ( 2 ) over a non‐Archimedean characteristic zero local field with odd residual characteristic. In this paper, we prove the equality between the local symmetric square L ‐function associated to π arising from integral representations and the corresponding Artin L ‐function for its Langlands parameter through the local Langlands correspondence. With this in hand, we show the stability of local symmetric γ‐factors attached to π under highly ramified twists.