Gupta, ShivajeeShivajeeGuptaVatwani, AkshaaAkshaaVatwani2025-08-282025-08-282022-11-01https://arxiv.org/abs/2211.02954https://d8.irins.org/handle/IITG2025/20118We 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 Gn00n.en-USRiesz type criteriaL-functionsSelberg classGrand Riemann hypothesisRamanujan-Hardy-Littlewood typee-Printe-Print123456789/555