Integrals Derived from the Doubling Method

Source abstract

Abstract In this note, we use a basic identity, derived from the generalized doubling integrals of [2], in order to explain the existence of various global Rankin–Selberg integrals for certain $L$-functions. To derive these global integrals, we use the identities relating Eisenstein series in [11], together with the process of exchanging roots. We concentrate on several well-known examples, and explain how to obtain them from the basic identity. Using these ideas, we also show how to derive a new global integral.