English

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 c(n)c(n) of the jj-function is limited to its asymptotic form. In this paper, we give the appropriate upper and lower bounds of c(n)c(n) to establish the inequalities associated with it.

Keywords

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}
}