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

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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 Hamburger, Hecke and 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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Acknowledgments

We wish to thank Sandro Bettin, Giuseppe Molteni, Stefano Vigni and the referee for carefully reading the paper and suggesting several improvements. The author is member of the GNAMPA group of INdAM.

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  1. Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146, Genova, Italy

    Alberto Perelli

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  1. Alberto Perelli
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Perelli, A. Converse theorems: from the Riemann zeta function to the Selberg class. Boll Unione Mat Ital 10, 29–53 (2017). https://doi.org/10.1007/s40574-016-0085-x

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