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

Manjil P. Saikia; Abhishek Sarma; Pranjal Talukdar

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

Number Theory 2023-02-06 v1

Authors: Manjil P. Saikia , Abhishek Sarma , Pranjal Talukdar

Abstract

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 modulo powers of primes for $k$ -tuples with $p$ -cores, where $p$ is a prime.

Keywords

Ramanujan-type congruences partition k-tuples 5-cores p-cores number theory infinite families

Cite

@article{arxiv.2302.01750,
  title  = {Ramanujan-type Congruences for Partition $k$-Tuples with $5$-Cores},
  author = {Manjil P. Saikia and Abhishek Sarma and Pranjal Talukdar},
  journal= {arXiv preprint arXiv:2302.01750},
  year   = {2023}
}

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