Arithmetic properties of the $\ell$-regular partitions

Suping Cui; Nancy Shanshan Gu

Arithmetic properties of the $\ell$-regular partitions

Combinatorics 2013-02-18 v1 Number Theory

Authors: Suping Cui , Nancy Shanshan Gu

Abstract

For a given prime $p$ , we study the properties of the $p$ -dissection identities of Ramanujan's theta functions $\psi(q)$ and $f(-q)$ , respectively. Then as applications, we find many infinite family of congruences modulo 2 for some $\ell$ -regular partition functions, especially, for $\ell=2,4,5,8,13,16$ . Moreover, based on the classical congruences for $p(n)$ given by Ramanujan, we obtain many more congruences for some $\ell$ -regular partition functions.

Keywords

partition congruences partition theory ramanujan identities and series

Cite

@article{arxiv.1302.3693,
  title  = {Arithmetic properties of the $\ell$-regular partitions},
  author = {Suping Cui and Nancy Shanshan Gu},
  journal= {arXiv preprint arXiv:1302.3693},
  year   = {2013}
}

Arithmetic properties of the $\ell$-regular partitions

Abstract

Keywords

Cite

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