Given an L-function F(s) from the extended Selberg class, we associate a function $\Phi_F(x,y)$. We show that the functions $\Phi_F(x,y)$ are, in the general case, the analogs of the modular forms associated with the GL(2) L-functions. Indeed, we prove that every $\Phi_F(x,y)$ is eigenfunction of a certain partial differential operator. Moreover, we prove a general correspondence theorem for such L-functions involving the functions $\Phi_F(x,y)$.

A correspondence theorem for L-functions and partial differential operators

PERELLI, ALBERTO
2011

Abstract

Given an L-function F(s) from the extended Selberg class, we associate a function $\Phi_F(x,y)$. We show that the functions $\Phi_F(x,y)$ are, in the general case, the analogs of the modular forms associated with the GL(2) L-functions. Indeed, we prove that every $\Phi_F(x,y)$ is eigenfunction of a certain partial differential operator. Moreover, we prove a general correspondence theorem for such L-functions involving the functions $\Phi_F(x,y)$.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/303440
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