Dirichlet Density Extends Asymptotic Density in Multiplicative Systems
نویسندگان
چکیده
Abstract. Dirichlet density extends global asymptotic density in an additive number system A whose generating series A(x) diverges at its radius of convergence (see [1], p. 50). This note shows that the parallel result holds for a multiplicative number system A, namely if the abcissa of convergence α of the generating series A(x) is finite and A(α) = ∞ then Dirichlet density extends global asymptotic density. Using this result it is proved that global asymptotic density ∆ satisifies ∆ (
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تاریخ انتشار 2007