Atul Dixit

activity

20242026

collaborators

7 papers

math.NT2026

A divisor function of Wigert and higher degree forms

Debika Banerjee, Atul Dixit, Rajat Gupta

Let $k \in N$ . Wigert's divisor function $d^{(\frac{1}{k})} (j)$ counts the number of representations of $j$ of the form $m^{k} + mn$ with $m \geq 1, n \geq 0$ . Let $\mat…

math.NT2026

Restricted Overpartitions and concave compositions: their modularity and asymptotics

Koustav Banerjee, Kathrin Bringmann, Atul Dixit

In this paper we study restricted overpartitions and concave compositions. In several cases the resulting generating functions involve simultaneously modular forms, mock theta func…

math.NT2025

Voronoi summation formula for the generalized divisor function $I ¨ _{z}^{(k)} (n)$

Atul Dixit, Bibekananda Maji, Akshaa Vatwani

For a fixed $z \in C$ and a fixed $k \in N$ , let $I ¨ _{z}^{(k)} (n)$ denote the sum of $z$ -th powers of those divisors $d$ of $n$ whose $k$ -th powers also divide $n$ . T…

math.CO2025

Some identities of the sums-of-tails type

Atul Dixit, Gaurav Kumar, Aviral Srivastava

A new sums-of-tails identity involving two parameters $b$ and $d$ is obtained and is used to derive more results of similar type. One of Ramanujan's sums-of-tails identities from t…

math.CO2025

Non-Rascoe partitions and a rank parity function associated to the Rogers-Ramanujan partitions

Atul Dixit, Gaurav Kumar, Aviral Srivastava

We study the generating function of the excess number of Rogers-Ramanujan partitions with odd rank over those with even rank, and, using combinatorial and analytical techniques, sh…

math.NT2025

On a function of Ramanujan twisted by a logarithm

Atul Dixit, Sumukha Sathyanarayana, N. Guru Sharan

A two-term functional equation for an infinite series involving the digamma function and a logarithmic factor is derived. A modular relation on page 220 of Ramanujan's Lost Noteboo…