AIMS Mathematics

2021, Issue 5: 4979-4988. doi: 10.3934/math.2021292
Research article

$\Omega$-result for the index of composition of an integral ideal

• Received: 10 August 2020 Accepted: 01 March 2021 Published: 03 March 2021
• MSC : 11N37

• Every nonzero integral ideal can be expressed as the product of finite prime ideals in Dedekind domain. For each integral ideal $\mathfrak{A}$, it is essential to measure the multiplicity of its prime ideal factors. We define $\lambda(\mathfrak{A}): = \frac{\log N(\mathfrak{A})}{\log \gamma(\mathfrak{A})}$ to be the index of composition of $\mathfrak{A}$, where $\gamma(\mathfrak{A}) = \prod_{\mathfrak{P}|\mathfrak{A}}N(\mathfrak{P})$ and $N(\mathfrak{A})$ is the norm of ideal $\mathfrak{A}$. In this paper, we obtain an $\Omega$-result for the mean value of the index of composition of integral ideal.

Citation: Jing Huang, Wenguang Zhai, Deyu Zhang. $\Omega$-result for the index of composition of an integral ideal[J]. AIMS Mathematics, 2021, 6(5): 4979-4988. doi: 10.3934/math.2021292

Related Papers:

• Every nonzero integral ideal can be expressed as the product of finite prime ideals in Dedekind domain. For each integral ideal $\mathfrak{A}$, it is essential to measure the multiplicity of its prime ideal factors. We define $\lambda(\mathfrak{A}): = \frac{\log N(\mathfrak{A})}{\log \gamma(\mathfrak{A})}$ to be the index of composition of $\mathfrak{A}$, where $\gamma(\mathfrak{A}) = \prod_{\mathfrak{P}|\mathfrak{A}}N(\mathfrak{P})$ and $N(\mathfrak{A})$ is the norm of ideal $\mathfrak{A}$. In this paper, we obtain an $\Omega$-result for the mean value of the index of composition of integral ideal.

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