Abhishek Sarma

activity

20222026

collaborators

6 papers

math.NT2026

Congruences for the Andrews--Uncu partition function $EO_{u} (n)$

Nayandeep Deka Baruah, Hirakjyoti Das, Manjil P. Saikia +1

In 2018, Andrews defined and studied the partition function $EO (n)$ , which counts the number of partitions of $n$ where each even part is less than each odd part. Thereaf…

math.NT2026

Proof of a Conjecture of Cui, Gu and Tang on 18-Colored Generalized Frobenius Partitions

Hirakjyoti Das, Hemjyoti Nath, Abhishek Sarma

Recently, the study of the number of $k$ -colored generalized Frobenius partitions, denoted by $c ϕ_{k} (n)$ , has witnessed renewed interest. In this paper, we investigate congruence pr…

math.NT2025

Sign Patterns and Congruences of certain infinite products involving the Rogers-Ramanujan continued fraction

Nayandeep Deka Baruah, Abhishek Sarma

We study the behavior of the signs of the coefficients of certain infinite products involving the Rogers-Ramanujan continued fraction. For example, if $$\sum_{n=0}^{\infty}A(n)q^{n…

math.NT2025

Congruences and density results for partitions into distinct even parts

Hemjyoti Nath, Abhishek Sarma

In this paper, we consider the set of partitions $p e d (n)$ which counts the number of partitions of $n$ wherein the even parts are distinct (and the odd parts are unrestricted). Usi…

math.NT2024

Arithmetic properties of $5$ -regular partitions into distinct parts

Nayandeep Deka Baruah, Abhishek Sarma

A partition is said to be $ℓ$ -regular if none of its parts is a multiple of $ℓ$ . Let $b_{5}^{'} (n)$ denote the number of 5-regular partitions into distinct parts (equivalent…

math.NT2022

Witness identities for three Ramanujan congruences

Nayandeep Deka Baruah, Hirakjyoti Das, Abhishek Sarma

For the unrestricted partition function $p (n)$ for integers $n \geq 0$ , it is known that $p (49 n + 19) \equiv 0 (mod 49)$ , $p (49 n + 33) \equiv 0 (mod 49)$ , and $p(49n + 40) \equiv…