Mean-value theorems for uniformly summable multiplicative functions on additive arithmetical semigroups. (English) Zbl 1326.11056
The authors give new characterizations for uniformly summable multiplicative functions over additive arithmetical semigroups (for the definition of uniform summable multiplicative functions over positive integers consult [the second author, Math. Z. 172, 255–271 (1980; Zbl 0416.10035); Period. Math. Hung. 17, 143–161 (1986; Zbl 0569.10024)]). The results improve those obtained in the PhD thesis of the first author [Uniformly summable multiplicative functions on additive arithmetical semigroups. Padeborn: Universität Paderborn (Diss.) (2011)] and of S. Wehmeier [Arithmetical semigroups. Paderborn: Universität Paderborn (Diss.) (2005)] and those given by W.-B. Zhang [Ramanujan J. 15, No. 1, 47–75 (2008; Zbl 1151.11051)].
Reviewer: Štefan Porubský (Praha)
MSC:
11N37 | Asymptotic results on arithmetic functions |
11T55 | Arithmetic theory of polynomial rings over finite fields |
30B30 | Boundary behavior of power series in one complex variable; over-convergence |