Riemann-type functional equations: Dirichlet polynomial approximations and a weak Gram law

We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, we improve upon results of Bombieri and Friedlander on Dirichlet polynomial approximations to L-functions and we prove that a generalized weak Gram law for the degree-one elements of the extended Selberg class is true infinitely often.