Abhishek Sarma

collaborators

3 papers

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.NT2023

Ramanujan-type Congruences for Partition $k$ -Tuples with $5$ -Cores

Manjil P. Saikia, Abhishek Sarma, Pranjal Talukdar

We prove several Ramanujan-type congruences modulo powers of $5$ for partition $k$ -tuples with $5$ -cores, for $k = 2, 3, 4$ . We also prove some new infinite families of congruences m…

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…

Arithmetic properties of 5-regular partitions into distinct parts

Ramanujan-type Congruences for Partition k-Tuples with 5-Cores

Witness identities for three Ramanujan congruences

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

Ramanujan-type Congruences for Partition $k$ -Tuples with $5$ -Cores