Cyclotomy, cyclotomic cosets and arithmetic properties of some families in $\frac{\mathbb{F}_l[x]}{\langle x^{p^sq^t}-1\rangle}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918109234855936 |
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| author | Zhou, Juncheng Wu, Hongfeng |
| author_facet | Zhou, Juncheng Wu, Hongfeng |
| contents | Arithmetic properties of some families in $\frac{\mathbb{F}_l[x]}{\langle x^{p^sq^t}-1\rangle}$ are obtained by using the cyclotomic classes of order 2 with respect to $n=p^sq^t$, where $p\equiv3 \mathrm{mod} 4$, $\gcd(ϕ(p^s),ϕ(q^t))=2$, $l$ is a primitive root modulo $q^t$ and $\mathrm{ord}_{p^s}(l)=ϕ(p^s)/2$. The form of these cyclotomic classes enables us to further generalize the results obtained in \cite{ref1}. The explicit expressions of primitive idempotents of minimal ideals in $\frac{\mathbb{F}_l[x]}{\langle x^{p^sq^t}-1\rangle}$ are also obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23179 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cyclotomy, cyclotomic cosets and arithmetic properties of some families in $\frac{\mathbb{F}_l[x]}{\langle x^{p^sq^t}-1\rangle}$ Zhou, Juncheng Wu, Hongfeng Number Theory Information Theory Arithmetic properties of some families in $\frac{\mathbb{F}_l[x]}{\langle x^{p^sq^t}-1\rangle}$ are obtained by using the cyclotomic classes of order 2 with respect to $n=p^sq^t$, where $p\equiv3 \mathrm{mod} 4$, $\gcd(ϕ(p^s),ϕ(q^t))=2$, $l$ is a primitive root modulo $q^t$ and $\mathrm{ord}_{p^s}(l)=ϕ(p^s)/2$. The form of these cyclotomic classes enables us to further generalize the results obtained in \cite{ref1}. The explicit expressions of primitive idempotents of minimal ideals in $\frac{\mathbb{F}_l[x]}{\langle x^{p^sq^t}-1\rangle}$ are also obtained. |
| title | Cyclotomy, cyclotomic cosets and arithmetic properties of some families in $\frac{\mathbb{F}_l[x]}{\langle x^{p^sq^t}-1\rangle}$ |
| topic | Number Theory Information Theory |
| url | https://arxiv.org/abs/2507.23179 |