On a Constant Related to the Prime Counting Function |
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| Authors: | Djamel Berkane Pierre Dusart |
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| Affiliation: | 1.Department of Mathematics,University of Blida,Blida,Algeria;2.XLIM UMR 7252, Faculté des sciences et techniques,Université de Limoges,Limoges Cedex,France |
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| Abstract: | Let ({pi(x)}) be the number of primes not exceeding x. We produce new explicit bounds for ({pi(x)}) and we use them to obtain a fine frame for the remainder term in the asymptotic formula of the sum ({sum_{2leq nleq x}1/pi(n)}). |
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