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On the Selberg class of Dirichlet series: small degrees

J. Brian Conrey·Amit Ghosh
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Abstract

In the study of Dirichlet series with arithmetic significance there has appeared (through the study of known examples) certain expectations, namely (i) if a functional equation and Euler product exists, then it is likely that a type of Riemann hypothesis will hold, (ii) that if in addition the function has a simple pole at the point s=1, then it must be a product of the Riemann zeta-function and another Dirichlet series with similar properties, and (iii) that a type of converse theorem holds, namely that all such Dirichlet series can be obtained by considering Mellin transforms of automorphic forms associated with arithmetic groups.

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J. Brian Conrey, Amit Ghosh. 1992-04-01. On the Selberg class of Dirichlet series: small degrees. https://doi.org/10.1215/s0012-7094-93-07225-0

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