|Author||Dixit, Atul ♦ Zaharescu, Alexandru ♦ Kim, Sun|
|Advisor||Berndt, Bruce C.|
|Publisher||American Mathematical Society|
|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.|
|Learning Resource Type||Article|
|Journal||Proceedings of the American Mathematical Society|
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