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

摘要

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.