In recent years, the log-concavity or log-convexity of combinatorial sequences and their root sequences, higher order Turán 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.
Zhongjie Li (Tue,) studied this question.