On the Selberg class of Dirichlet series: small weights
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 zetafunction 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 1992
 arXiv:
 arXiv:math/9204217
 Bibcode:
 1992math......4217C
 Keywords:

 Mathematics  Number Theory