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Riesz-type criteria for L-functions in the Selberg class
Published online by Cambridge University Press: 29 May 2023
Abstract
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 ${G^{n , 0}_{0 , n}}$.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society
Footnotes
The first author was supported by the Shyama Prasad Mukherjee fellowship CSIR SPM-06/1031(0281)/2018-EMR-I. The second author was supported by the MHRD SPARC project SPARC/2018-2019/P567/SL, the SERB-DST grant ECR/2018/001566, and the DST INSPIRE Faculty Award Program DST/INSPIRE/Faculty/Batch-13/2018.
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