Rajat Gupta

activity

20232026

collaborators

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

math.CO2024

Partitions in which every term but the smallest one is consecutive

Rajat Gupta, Noah Lebowitz-Lockard

In this article, we introduce the notion of almost consecutive partitions. A partition is almost consecutive if every term is consecutive, with the possible exception of the smalle…

math.NT2024

On the $k$ th smallest part of a partition into distinct parts

Rajat Gupta, Noah Lebowitz-Lockard, Joseph Vandehey

A classic theorem of Uchimura states that the difference between the sum of the smallest parts of the partitions of $n$ into an odd number of distinct parts and the corresponding s…

math.CO2023

Non-standard binary representations and the Stern sequence

Katie Anders, Madeline Locus Dawsey, Rajat Gupta +1

We show that the number of short binary signed-digit representations of an integer $n$ is equal to the $n$ -th term in the Stern sequence. Various proofs are provided, including dir…