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
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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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
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