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Comparison of regular convolutions. (English) Zbl 0668.10012
The author defines a family of equivalence relations in the class of all regular convolutions [as defined by the reviewer, Colloq. Math. 10, 81-94 (1963; Zbl 0114.265)]. This family includes a relation studied by P. J. McCarthy [Port. Math. 27, 1-13 (1968; Zbl 0203.353)]. These relations are then applied to a study of generalized Ramanujan sums [as defined by V. Sita Ramaiah, J. Reine Angew. Math. 303/304, 265-283 (1978; Zbl 0391.10007)] and A-k-primitive functions [defined in the case of Dirichlet convolution by E. Cohen, Duke Math. J. 25, 401-421 (1958; Zbl 0082.036)].
Reviewer: W.Narkiewicz

MSC:
11A25 Arithmetic functions; related numbers; inversion formulas
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