A general positivity result on coefficients of certain $q$-series
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917852745826304 |
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| author | Liu, Ji-Cai |
| author_facet | Liu, Ji-Cai |
| contents | 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 $q$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19907 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A general positivity result on coefficients of certain $q$-series Liu, Ji-Cai Number Theory Combinatorics 05A17, 05A20 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 $q$-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. |
| title | A general positivity result on coefficients of certain $q$-series |
| topic | Number Theory Combinatorics 05A17, 05A20 |
| url | https://arxiv.org/abs/2409.19907 |