Atul Dixit

activity

20242026

collaborators

Showing math.NTShow all

6 papers · 1 filter

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.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…

math.NT2024

The Rogers-Ramanujan dissection of a theta function

Atul Dixit, Gaurav Kumar

Page 27 of Ramanujan's Lost Notebook contains a beautiful identity which not only gives, as a special case, a famous modular relation between the Rogers-Ramanujan functions $G (q)$ …