Riesz-type criteria for <i>L</i>-functions in the Selberg class

Abstract We formulate a generalization of Riesz-type criteria in the setting L -functions belonging to Selberg class. obtain criterion which is sufficient for grand Riemann hypothesis (GRH) satisfying axioms class without imposing Ramanujan on their coefficients. also construct subclass and prove necessary GRH this subclass. Identities Ramanujan–Hardy–Littlewood type are established setting, specific cases yield new transformation formulas involving special values Meijer G -function ${G^{n , 0}_{0 n}}$ .