On a theorem of A. I. Popov on sums of squares

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dc.contributor.author Dixit, Atul
dc.contributor.author Berndt, Bruce C.
dc.contributor.author Kim, Sun
dc.contributor.author Zaharescu, Alexandru
dc.date.accessioned 2016-11-08T12:20:20Z
dc.date.available 2016-11-08T12:20:20Z
dc.date.issued 2016-10
dc.identifier.citation Berndt, Bruce C.; Dixit, Atul; Kim, Sun and Zaharescu, Alexandru, “On a theorem of A. I. Popov on sums of squares”, arXiv, Cornell University Library, DOI: arXiv:1610.05840, Oct. 2016. en_US
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/2520
dc.identifier.uri http://arxiv.org/abs/1610.05840
dc.description.abstract Let rk(n) denote the number of representations of the positive integer n as the sum of k squares. In 1934, the Russian mathematician A. I. Popov stated, but did not rigorously prove, a beautiful series transformation involving rk(n) and certain Bessel functions. We provide a proof of this identity for the first time, as well as for another identity, which can be regarded as both an analogue of Popov’s identity and an identity involving r2(n) from Ramanujan’s lost notebook.
dc.description.statementofresponsibility by Bruce C. Berndt, Atul Dixit, Sun Kim and Alexandru Zaharescu
dc.language.iso en_US en_US
dc.publisher Cornell University Library en_US
dc.title On a theorem of A. I. Popov on sums of squares en_US
dc.type Article en_US

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