On the triple product L-function for GL_3xGL_3xGL_n

Motivated by conjectures of Braverman-Kazhdan, L. Lafforgue, Ngô and Sakellaridis, we prove an automorphic-twisted summation formula for pairs of quadratic space. We also speculate on the application of this summation formula to showing the functional equation of the Langlands triple L-function for GL_3xGL_3xGL_n.