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arXiv · 2401.05853

On the cyclotomic field $\mathbb{Q}(e^{2\pi {\bf i}/p})$ and Zhi-Wei Sun's conjecture on $\det M_p$

Li-Yuan Wang·Hai-Liang Wu
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Abstract

In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. In this paper, by using the arithmetic properties of $p$-th cyclotomic field and the finite field $\mathbb{F}_p$, we confirm this conjecture.

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Li-Yuan Wang, Hai-Liang Wu. 2024-01-11. On the cyclotomic field $\mathbb{Q}(e^{2\pi {\bf i}/p})$ and Zhi-Wei Sun's conjecture on $\det M_p$. https://doi.org/10.1016/j.ffa.2024.102533

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