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This is a Quantitative Study study.

October 2, 2025Open Access

Inequalities related to the coefficients of the j-function

Key Points

Upper and lower bounds for the Fourier coefficient c(n) are established.
The study explores inequalities related to the j-function and its Fourier coefficient.
It highlights the limited research on combinatorial sequences and their inequalities.
It connects the findings to Turán and Laguerre inequalities in combinatorial mathematics.

Abstract

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.

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Cite This Study

Zhongjie Li (Tue,) studied this question.

synapsesocial.com/papers/68de84bf5b556a9128e1bdc2 https://doi.org/https://doi.org/10.48550/arxiv.2506.19292

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