This is an expanded version of the author's lecture at the XX Congresso U.M.I., held in Siena in September 2015. After a brief review of $L$-functions, we turn to the classical converse theorems of H.Hamburger, E.Hecke and A.Weil, and to some later developments. Finally we present several results on converse theorems in the framework of the Selberg class of $L$-functions.

Converse theorems: from the Riemann zeta function to the Selberg class

PERELLI, ALBERTO
2017

Abstract

This is an expanded version of the author's lecture at the XX Congresso U.M.I., held in Siena in September 2015. After a brief review of $L$-functions, we turn to the classical converse theorems of H.Hamburger, E.Hecke and A.Weil, and to some later developments. Finally we present several results on converse theorems in the framework of the Selberg class of $L$-functions.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/840315
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