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

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dc.contributor.advisor Berndt, Bruce C.
dc.contributor.author Dixit, Atul
dc.contributor.author Kim, Sun
dc.contributor.author Zaharescu, Alexandru
dc.date.accessioned 2017-04-18T10:39:01Z
dc.date.available 2017-04-18T10:39:01Z
dc.date.issued 2017-04
dc.identifier.citation Berndt, Bruce C.; Dixit, Atul; Kim, Sun and Zaharescu, Alexandru, “On a theorem of A. I. Popov on sums of squares”, Proceedings of the American Mathematical Society, DOI: 10.1090/proc/13547, Apr. 2017. en_US
dc.identifier.issn 1088-6826
dc.identifier.issn 0002-9939
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/2873
dc.identifier.uri http://dx.doi.org/10.1090/proc/13547
dc.description.abstract Let $ r_k(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 $ r_k(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 $ r_2(n)$ from Ramanujan's lost notebook. en_US
dc.description.statementofresponsibility by Bruce C. Berndt, Atul Dixit, Sun Kim and Alexandru Zaharescu
dc.format.extent Vol. 145, no. 9, pp. 3795-3808
dc.language.iso en_US en_US
dc.publisher American Mathematical Society en_US
dc.title On a theorem of A. I. Popov on sums of squares en_US
dc.type Article en_US
dc.relation.journal Proceedings of the American Mathematical Society

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