算术半群的Alladi公式的推广
Generalizations of Alladi's formula for arithmetical semigroups
摘要：
本文证明了具有Dirichlet卷积的Alladi公式的一般形式对满足公理$A$或公理$A^{\#}$的算术半群成立.作为应用，我们将主要结果应用于某些来自代数数论、算术几何和图论的半群，特别推广了Wang 2021，Kural et al. 2020和Duan et al. 2020的结果.
英文摘要：
In this article, we prove that a general version of Alladi's formula with Dirichlet convolution holds for arithmetical semigroups satisfying Axiom $A$ or Axiom $A^{\#}$. As applications, we apply our main results to certain semigroups coming from algebraic number theory, arithmetical geometry and graph theory, particularly generalizing the results of Wang 2021, Kural et al. 2020 and Duan et al. 2020.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
