On the positive coefficients of two families of $q$-series
| Title: | On the positive coefficients of two families of $q$-series |
|---|---|
| Authors: | Liu, Ji-Cai, Liao, Kong-Lian |
| Publication Year: | 2024 |
| Collection: | Mathematics |
| Subject Terms: | Mathematics - Number Theory, Mathematics - Combinatorics, 11S05, 05A17, 05A20 |
| More Details: | Let $S$ be a finite set of pairwise coprime positive integers and $Ax^2+Bx$ be an integer valued polynomial with $A> B\ge 0$. For integers $k\ge 1$ and $n\ge 0$, the coefficients $\gamma_{S,A,B}^k (n)$ are defined as \begin{align*} \prod_{s\in S}\frac{1}{1-q^s}\sum_{j\not\in [-k,k-1]} (-1)^{j+k}q^{Aj^2+Bj}=\sum_{n= 0}^{\infty}\gamma_{S,A,B}^k (n)q^n. \end{align*} In this paper, we investigate the positivity of $\gamma_{S,A,B}^k (n)$ for $|S|=4,5$. Comment: 20 pages |
| Document Type: | Working Paper |
| Access URL: | http://arxiv.org/abs/2411.04726 |
| Accession Number: | edsarx.2411.04726 |
| Database: | arXiv |
| Description not available. |