Gupta, ShivajeeShivajeeGuptaVatwani, AkshaaAkshaaVatwani2025-08-312025-08-312024-06-2910.4153/S0008414X230003542-s2.0-85162057503https://d8.irins.org/handle/IITG2025/26424We formulate a generalization of Riesz-type criteria in the setting of L-functions belonging to the Selberg class. We obtain a criterion which is sufficient for the grand Riemann hypothesis (GRH) for L-functions satisfying axioms of the Selberg class without imposing the Ramanujan hypothesis on their coefficients. We also construct a subclass of the Selberg class and prove a necessary criterion for GRH for L-functions in this subclass. Identities of Ramanujan-Hardy-Littlewood type are also established in this setting, specific cases of which yield new transformation formulas involving special values of the Meijer G-function of the type.false11M06 11M26 11M41 33C20Article1062-108829 June 20241arJournal1WOS:001019433400001