7 papers
Untrodden pathways in the study of partitions with parts separated by parity
Nargish Punia, Rahul Kumar
In this paper, we study a partition function with parts separated by parity from a family of partition functions introduced by Andrews in 2019. We first show that its generating fu…
Irreducibility and weak spectral gap in free product von Neumann algebras
Aldo Garcia Guinto, Fehmi Ekin Giritlioglu, Rahul Kumar R. +2
Consider a free product of non-trivial von Neumann algebras. Using amalgamated free product techniques, we establish irreducibility and weak spectral…
On Partition Classes Arising from Parity, Differences, and Repeated Smallest Parts
Rahul Kumar, Nargish Punia
In this paper, we study various classes of partition functions such as those related to the parity of the number of parts, to differences of partition numbers, and to partitions wi…
On Euler's Theorem
George E. Andrews, Rahul Kumar, Ae Ja Yee
Euler's theorem asserts that where is the number of partitions of into distinct parts and is the number of partitions of into odd parts. In this p…
Rank, two-color partitions and Mock theta function
George E. Andrews, Rahul Kumar
In this paper, we establish that the number of partitions of a natural number with positive odd rank is equal to the number of two-color partitions (red and blue), where the smalle…
A family of integrals related to values of the Riemann zeta function
Rahul Kumar, Paul Levrie, Jean-Christophe Pain +1
We propose a relation between values of the Riemann zeta function and a family of integrals. This results in an integral representation for , where is a positive int…
Operator-Valued Twisted Araki-Woods Algebras
Rahul Kumar R, Melchior Wirth
We introduce operator-valued twisted Araki-Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes -Gaussian and -Araki-Wo…