abstract:In the mathematical theory of automorphic forms, a converse theorem gives sufficient conditions for a Dirichlet series to be the Mellin transform of a modular form. More generally a converse theorem states that a representation of an algebraic group over the adeles is automorphic whenever the L-functions of various twists of it are well behaved.
This articleexplicitlyexpressedconversetheoremof the inverse function differentialprinciple, Based onthistheorem, the author proposedonekind ofintegration, then gave some examples.