On the \(\psi\)-product of D. H. Lehmer
\textit{D. H. Lehmer} [Trans. Am. Math. Soc. 33, 945-957 (1931; Zbl 0003.10202)] considered a class of multiplications defined in the set F of all arithmetic functions which obey five axioms, assuring that F becomes a commutative ring with unity with usual addition. The author notes that the exponential convolution considered by \textit{P. Erdős} and \textit{M. V. Subbarao} [Lect. Notes Math. 251, 119-125 (1972; Zbl 0228.10033)] does not obey all Lehmer's axioms and shows how to modify them so that the exponential convolution as well as many other convolutions used in number theory satisfy them.
scientific article; zbMATH DE number 3972939