Inequalities related to the coefficients of the $j$-function
Combinatorics
2025-06-25 v1 Number Theory
Abstract
In recent years, the log-concavity or log-convexity of combinatorial sequences and their root sequences, higher order Tur{\'a}n inequalities, and Laguerre inequalities of order two have been widely studied. However, the research of the Fourier coefficient of the -function is limited to its asymptotic form. In this paper, we give the appropriate upper and lower bounds of to establish the inequalities associated with it.
Cite
@article{arxiv.2506.19292,
title = {Inequalities related to the coefficients of the $j$-function},
author = {Zhongjie Li},
journal= {arXiv preprint arXiv:2506.19292},
year = {2025}
}