| 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 |