On some q-series identities related to a generalized divisor function and their implications

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dc.contributor.author Gupta, Rajat
dc.contributor.author Kumar, Rahul
dc.coverage.spatial United Sates of America
dc.date.accessioned 2012-09-19T16:39:14Z
dc.date.available 2012-09-19T16:39:14Z
dc.date.issued 2021-11
dc.identifier.citation Gupta, Rajat and Kumar, Rahul, "On some q-series identities related to a generalized divisor function and their implications", Discrete Mathematics, DOI: 10.1016/j.disc.2021.112559, vol. 344, no. 11, Nov. 2021. en_US
dc.identifier.issn 0012-365X
dc.identifier.uri https://doi.org/10.1016/j.disc.2021.112559
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/6805
dc.description.abstract In this article, a q-series examined by Kluyver and Uchimura is generalized. This allows us to find generalization of the identities in the random acyclic digraph studied by Simon, Crippa, and Collenberg in 1993. As one of the corollaries of our main theorem, we get results of Dilcher and Andrews, Crippa, and Simon. This main theorem involves a surprising new generalization of the divisor function ?s(n), which we denote by ?s,z(n). Analytic properties of ?s,z(n) are also studied. As a special case of one of our theorem we obtain result from a recent paper of Bringmann and Jennings-Shaffer.
dc.description.statementofresponsibility by Rajat Gupta and Rahul Kumar
dc.format.extent vol. 344, no. 11
dc.language.iso en_US en_US
dc.publisher Elsevier en_US
dc.subject q-Series en_US
dc.subject Partition identities en_US
dc.subject Divisor function en_US
dc.subject Average orders en_US
dc.title On some q-series identities related to a generalized divisor function and their implications en_US
dc.type Article en_US
dc.relation.journal Discrete Mathematics


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