201309.7467v2 Cuspidal part of an Eisenstein series restricted to an index 2 subfield

Let E be a quadratic extension of a number field F. Let E(g, s) be an Eisenstein serieson GL2(E), and let F be a cuspidal automorphic form on GL2(F). We will consider in this paper thefollowing automorphic integral:This is in some sense the complementary case to the well-known Rankin-Selberg integral and thetriple product formula. We will ap..