23 citations · 35 across the 50 of their papers we have counts for
5 papers · 1 filter
On a theorem of A. I. Popov on sums of squares
Bruce C. Berndt, Atul Dixit, Sun Kim +1
Let denote the number of representations of the positive integer as the sum of squares. In 1934, the Russian mathematician A.~I.~Popov stated, but did not rigorous…
New pathways and connections in Number Theory and Analysis motivated by two incorrect claims of Ramanujan
Bruce C. Berndt, Atul Dixit, Arindam Roy +1
We focus on three pages in Ramanujan's lost notebook, pages 336, 335, and 332, in decreasing order of attention. On page 336, Ramanujan proposes two identities, but the formulas ar…
New representations for via reciprocity theorems
Koustav Banerjee, Atul Dixit
Two new representations for Ramanujan's function are obtained. The proof of the first one uses the three-variable reciprocity theorem due to Soon-Yi Kang and a transformatio…
Error functions, Mordell integrals and an integral analogue of partial theta function
Atul Dixit, Arindam Roy, Alexandru Zaharescu
A new transformation involving the error function , the imaginary error function , and an integral analogue of a partial theta function is given…
Overpartitions related to the mock theta function
George E. Andrews, Atul Dixit, Daniel Schultz +1
It was recently shown that , where is one of the third order mock theta functions, is the generating function of , the number of partitions of a positive inte…