Mathematics
http://repository.iitgn.ac.in/handle/123456789/547
2017-04-26T15:47:08ZNew representations for σ(q) via reciprocity theorems
http://repository.iitgn.ac.in/handle/123456789/2883
New representations for σ(q) via reciprocity theorems
Banerjee, Koustav; Dixit, Atul
2016-03-17T00:00:00ZOn a theorem of A. I. Popov on sums of squares
http://repository.iitgn.ac.in/handle/123456789/2873
On a theorem of A. I. Popov on sums of squares
Berndt, Bruce C..; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru
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.
2017-04-01T00:00:00ZExistence of solutions to fully nonlinear elliptic equations with gradient nonlinearity
http://repository.iitgn.ac.in/handle/123456789/2852
Existence of solutions to fully nonlinear elliptic equations with gradient nonlinearity
Tyagi, Jagmohan; Verma, Ram Baran
2017-04-01T00:00:00ZRegular sequences from determinantal conditions
http://repository.iitgn.ac.in/handle/123456789/2719
Regular sequences from determinantal conditions
Saha, Joydip; Sengupta, Indranath; Tripathi, Gurab
2017-03-01T00:00:00Z