Generalizations of Alladi's formula for arithmetical semigroups

Abstract

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.

Some minor changes. Published online in The Ramanujan Journal

References in corpus (1)

• On partial sums of the Möbius and Liouville functions for number fields

Cited by in corpus (1)

• Dynamics on the number of prime divisors for additive arithmetic semigroups