Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Sharper bounds for the Chebyshev functions $ \theta (x)$ and $ \psi (x)$. II


Author: Lowell Schoenfeld
Journal: Math. Comp. 30 (1976), 337-360
MSC: Primary 10H05
Corrigendum: Math. Comp. 30 (1976), 900.
Corrigendum: Math. Comp. 30 (1976), 900.
MathSciNet review: 0457374
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Abstract: In this paper, bounds given in the first part of the paper are strengthened. In addition, it is shown that the interval $ (x,x + x/16597)$ contains a prime for all $ x \geqslant 2,010,760$; and explicit bounds for the Chebyshev functions are given under the assumption of the Riemann hypothesis.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0457374-X
Article copyright: © Copyright 1976 American Mathematical Society