Geodesic
Riesz-type criteria for L-functions in the Selberg class
Canadian journal of mathematics, Tome 76 (2024) no. 3, pp. 1062-1088

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DOI

We 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 ${G^{n , 0}_{0 , n}}$.
DOI : 10.4153/S0008414X23000354
Mots-clés : Selberg class, grand Riemann hypothesis, Riesz-type criteria, modular relations 
Gupta, Shivajee; Vatwani, Akshaa. Riesz-type criteria for L-functions in the Selberg class. Canadian journal of mathematics, Tome 76 (2024) no. 3, pp. 1062-1088. doi: 10.4153/S0008414X23000354
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     title = {Riesz-type criteria for {L-functions} in the {Selberg} class},
     journal = {Canadian journal of mathematics},
     pages = {1062--1088},
     year = {2024},
     volume = {76},
     number = {3},
     doi = {10.4153/S0008414X23000354},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X23000354/}
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