On additive and multiplicative arithmetical functions
Masood Aryapoor
TL;DR
This paper characterizes multiplicative and additive arithmetical functions and demonstrates an isomorphism between their groups, providing a foundational understanding of their algebraic structure.
Contribution
It introduces a new characterization of these functions and proves the isomorphism between their groups, advancing the theoretical framework of arithmetical functions.
Findings
The group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.
A new characterization of multiplicative and additive arithmetical functions is provided.
The algebraic structure of these functions is clarified through the isomorphism.
Abstract
A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.
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Taxonomy
TopicsAdvanced Mathematical Identities · Computability, Logic, AI Algorithms · semigroups and automata theory