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<p>In the ring of arithmetic functions, several characterizations of multiplicative /completely multiplicative and additive /completely additive functions are established. They are derived by employing concepts related to unitary convolution, including generalized unitary Möbius functions and logarithmic and exponential operators. The distributivity of arithmetic functions through discriminative products is also investigated, leading to unitary analogues of classical results obtained via the Dirichlet convolution. These results provide necessary and/or sufficient conditions for multiplicative/ completely multiplicative, and additive /completely additive behavior, extending earlier studies.</p>

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Characterizing multiplicative and additive functions through the use of unitary convolution

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Pussadee Yangklan,
  • Vichian Laohakosol

摘要

In the ring of arithmetic functions, several characterizations of multiplicative /completely multiplicative and additive /completely additive functions are established. They are derived by employing concepts related to unitary convolution, including generalized unitary Möbius functions and logarithmic and exponential operators. The distributivity of arithmetic functions through discriminative products is also investigated, leading to unitary analogues of classical results obtained via the Dirichlet convolution. These results provide necessary and/or sufficient conditions for multiplicative/ completely multiplicative, and additive /completely additive behavior, extending earlier studies.