Mauclaire, Jean-Loup Deux résultats de théorie probabiliste des nombres. (Two results in probabilistic number theory). (French) Zbl 0766.11036 C. R. Acad. Sci., Paris, Sér. I 311, No. 2, 69-72 (1990). An arithmetic semigroup is a normed semigroup such that \(\sum_{a\in A, N(a)\leq x} 1=LX+o(x)\) with some constant \(L>0\). The first result asserts that the Turán-Kubilius inequality may fail in such a semigroup, even in the following strong sense: every arithmetic semigroup has an extension in which the T-K inequality fails. The second result is a generalization of a theorem of Elliott on the moments of Ramanujan’s \(\tau\) function. The results are announced without proof. Reviewer: I.Z.Ruzsa (Budapest) Cited in 1 Review MSC: 11K99 Probabilistic theory: distribution modulo \(1\); metric theory of algorithms 11K65 Arithmetic functions in probabilistic number theory 11N45 Asymptotic results on counting functions for algebraic and topological structures 11N80 Generalized primes and integers Keywords:arithmetic semigroup; Turán-Kubilius inequality; moments of Ramanujan’s \(\tau\) function PDFBibTeX XMLCite \textit{J.-L. Mauclaire}, C. R. Acad. Sci., Paris, Sér. I 311, No. 2, 69--72 (1990; Zbl 0766.11036)