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Author Dixit, Atul ♦ Zaharescu, Alexandru ♦ Kim, Sun
Advisor Berndt, Bruce C.
Source IIT Gandhinagar
Content type Text
Publisher American Mathematical Society
Language English
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.
ISSN 10886826
Learning Resource Type Article
Publisher Date 2017-04-01
e-ISSN 00029939
Journal Proceedings of the American Mathematical Society
Volume Number 145
Issue Number 9
Starting Page 3795
Ending Page 3808


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