The Zoo of Integral Representations for L-functions

Automorphic L-functions, initially defined on some right half plane, are conjectured to be have meromorphic continuation to the whole complex plane. An effective method to prove this in some cases is by using an integral representation. Since the 1960’s, many such integrals were discovered, some of them representing the same L-function, but seemingly unrelated. Using recent discoveries of D.Ginzburg and D. Soudry, I will explain the relation between different integrals representing the same L-function.