Generalizations of Alladi’s formula for arithmetical semigroups

Generalizations of Alladi’s formula for arithmetical semigroups

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 t...

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Veröffentlicht in:The Ramanujan journal 2022-08, Vol.58 (4), p.1285-1319
Hauptverfasser: Duan, Lian, Ma, Ning, Yi, Shaoyun
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Dirichlet problem
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Graph theory
Mathematics
Mathematics and Statistics
Number Theory
Semigroups
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Zusammenfassung: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.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-021-00531-7