caa a22 4500 467989540 CHVBK 20180323112541.0 cr unu---uuuuu 170328e19900301xx s 000 0 ger 10.1007/BF01571278 doi (NATIONALLICENCE)springer-10.1007/BF01571278 Wolke Dieter Mathematisches Institut der Universität, Albertstraße 23b, D-7800, Freiburg, Bundesrepublik Deutschland aut Über die Primteiler-Anzahl ω( n ) [Elektronische Daten] [Dieter Wolke] On the prime divisor function ω( n ) It is shown by analytical means that, if one assumes the Riemann hypothesis, the asymptotic formula $$\sum\limits_{n \leqslant x} {\omega (n) = x 1n1n } x + B - x\int_l^{x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } {\frac{{\{ t\} }}{{t^2 (1n x - 1n t)}}dt + O(x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2} + \varepsilon } )} $$ holds. This improves a result ofB. Saffari, who got a weaker error term by using the Dirichlet "hyperbola method”. The above formula, in turn, implies the Riemann hypothesis. Springer-Verlag, 1990 Monatshefte für Mathematik Springer-Verlag 110/1(1990-03-01), 73-78 0026-9255 110:1<73 1990 110 605 https://doi.org/10.1007/BF01571278 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01571278 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wolke Dieter Mathematisches Institut der Universität, Albertstraße 23b, D-7800, Freiburg, Bundesrepublik Deutschland aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer-Verlag 110/1(1990-03-01), 73-78 0026-9255 110:1<73 1990 110 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer