Rajat Gupta

activity

20242026

collaborators

5 papers

math.NT2026

Ramanujan's and Lim's Identities and Harmonic Maass--Jacobi Forms

Kathrin Bringmann, Rajat Gupta, Badri Vishal Pandey

We study an extension of Ramanujan's identities for odd zeta values by Lim and introduce Jacobi analogues of classical Eichler integrals of Eisenstein series. In negative weight we…

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.NT2025

Summation formulas for Hurwitz class numbers and other mock modular coefficients

Olivia Beckwith, Nikolaos Diamantis, Rajat Gupta +2

We prove a formula for weighted sums of the first $n$ coefficients of mock modular forms of moderate growth and apply it to Hurwitz class numbers and coefficients of negative half…

math.NT2025

Non-standard quaternary representations and the Fibonacci numbers

Katie Anders, Madeline L. Dawsey, Rajat Gupta +2

Let $f_{4} (n)$ be the number of hyperquaternary representations of $n$ and $b_{4} (n)$ be the number of balanced quaternary representations of $n$ . We show that there is no integer $k$ …

math.NT2024

A segment of Euler product associated to a certain Dirichlet series

Rajat Gupta, Aditi Savalia

In the spirit of the work of Hardy-Littlewood and Lavrik, we study the Dirichlet series associated to the generalized divisor function $I ¨ _{I^} \pm (n) := \sum_{d ∣ n} d^{I^} \pm$ . We obtain an exac…