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| Authors: | Pierre Dusart. |
| Affiliation: | LACO, ESA 6090, Faculté des Sciences, 123 avenue Albert Thomas, 87060 Limoges Cedex, FRANCE |
| Abstract: | ROSSER and SCHOENFELD have used the fact that the first 3,500,000 zeros of the RIEMANN zeta function lie on the critical line to give estimates on  and  . With an improvement of the above result by BRENTet al., we are able to improve these estimates and to show that the  prime is greater than  for  . We give further results without proof. |
| Keywords: | Distribution of primes arithmetic functions |
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