English

A further look at the truncated pentagonal number theorem

Number Theory 2018-08-02 v1 Combinatorics

Abstract

In this paper, we study the asymptotic behavior of the following function Mk(n):=(1)k1j=0k1(p(nj(3j+1)/2)p(nj(3j+5)/21)),M_k(n):=(-1)^{k-1} \sum_{j=0}^{k-1}\big(p(n-j(3j+1)/2)-p(n-j(3j+5)/2-1)\big), which arises from Andrews and Merca's truncated pentagonal number theorem.

Keywords

Cite

@article{arxiv.1808.00227,
  title  = {A further look at the truncated pentagonal number theorem},
  author = {Shane Chern},
  journal= {arXiv preprint arXiv:1808.00227},
  year   = {2018}
}
R2 v1 2026-06-23T03:21:20.521Z