Some remarks on the convergence of the Dirichlet series of L-functions

J. Kaczorowski, A. Perelli

Published 2015-06-25Version 1

We show that the abscissae of uniform and absolute convergence of Dirichlet series coincide in the case of L-functions from the Selberg class. We also study, by means of a suitably defined lift operator, the abscissa of absolute convergence inside the extended Selberg class. Our results indicate that the behavior of such an abscissa is quite different in the two classes.