| 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 |
|