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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.19292 |
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Table of 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.