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Mathematics of Computation

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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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Article copyright: © Copyright 1976 American Mathematical Society