Geodesic
A Note on Dirichlet Convolutions
Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 457-462

Voir la notice de l'article provenant de la source Cambridge University Press

In [3] Rubel proved that if h(n) is an arithmetic function such that , L finite, then where μ(n) is the Mobius function. This result was extended to functions other than μ(n) in [4]; however, (as first pointed out to the author by Benjamin Volk), the order condition imposed there is unnecessary; in fact, utilizing the result of [3], the following slightly more general theorem has an almost trivial proof. 
Segal, S. L. A Note on Dirichlet Convolutions. Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 457-462. doi: 10.4153/CMB-1966-055-8
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[1] 1. Landau, E., Handbuch der Lehre von der Verteilung der Primzahlen, reprinted with an appendix by Paul Bateman, Chelsea, (1953). Google Scholar

[2] 2. Prachar, K., Primzahlverteilung. Springer, Berlin, (1957) Google Scholar

[3] 3. Rubel, L.A., An Abelian Theorem for Number-Theoretic Sums. Acta Arith. 6, (1960) pages 175-177, correction Acta Arith. 6, (1961), page 523. Google Scholar

[4] 4. Segal, S. L., Dirichlet convolutions and the Silvèrman- Toeplitz conditions. Acta Arith. 10, (1964), pages 287-291. Google Scholar

[5] 5. Segal, S. L., On Ingham's Summation Method. Can. Journ. Math. 18, (1966), pages 97-105. Google Scholar

[6] 6. Segal, S. L., Summability by Dirichlet Convolutions. Submitted for publication. Google Scholar

[7] 7. Titchmarsh, E. C., The Theory of the Riemann Zeta- Function. Oxford, (1951). Google Scholar

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