Rajat Gupta

activity

20242026

collaborators

4 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.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 $σ_{α} (n) := \sum_{d ∣ n} d^{α}$ . We obtain an exact i…