A general positivity result on coefficients of certain $q$-series
Number Theory
2024-12-03 v3 Combinatorics
Abstract
Based on a classical result on partitions of an integer into a finite set of positive integers, we establish a general positivity result on coefficients of certain -series which uniformly refines the positivity of truncated pentagonal number series, truncated Gauss' identities and some special cases of truncated Jacobi triple product identity. As an application, we prove two positivity conjectures due to Merca.
Keywords
Cite
@article{arxiv.2409.19907,
title = {A general positivity result on coefficients of certain $q$-series},
author = {Ji-Cai Liu},
journal= {arXiv preprint arXiv:2409.19907},
year = {2024}
}
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24 pages