We prove that every functional equation of Riemann's type has infinitely many linearly independent solutions in the set of generalized Dirichlet series. This shows that the degree conjecture in the Selberg class theory depends heavily on the hypothesis that its elements are ordinary Dirichlet series.
A remark on solutions of functional equations of Riemann's type
PERELLI, ALBERTO
2004-01-01
Abstract
We prove that every functional equation of Riemann's type has infinitely many linearly independent solutions in the set of generalized Dirichlet series. This shows that the degree conjecture in the Selberg class theory depends heavily on the hypothesis that its elements are ordinary Dirichlet series.
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