Inequalities related to the coefficients of the $j$-function
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911020355682304 |
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| author | Li, Zhongjie |
| author_facet | Li, Zhongjie |
| contents | In recent years, the log-concavity or log-convexity of combinatorial sequences and their root sequences, higher order Tur{á}n inequalities, and Laguerre inequalities of order two have been widely studied. However, the research of the Fourier coefficient $c(n)$ of the $j$-function is limited to its asymptotic form. In this paper, we give the appropriate upper and lower bounds of $c(n)$ to establish the inequalities associated with it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19292 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inequalities related to the coefficients of the $j$-function Li, Zhongjie Combinatorics Number Theory In recent years, the log-concavity or log-convexity of combinatorial sequences and their root sequences, higher order Tur{á}n inequalities, and Laguerre inequalities of order two have been widely studied. However, the research of the Fourier coefficient $c(n)$ of the $j$-function is limited to its asymptotic form. In this paper, we give the appropriate upper and lower bounds of $c(n)$ to establish the inequalities associated with it. |
| title | Inequalities related to the coefficients of the $j$-function |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2506.19292 |