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# Sharper Bounds for the Chebyshev Functions $\theta(x)$ and $\psi(x)$. II

Lowell Schoenfeld
Mathematics of Computation
Vol. 30, No. 134 (Apr., 1976), pp. 337-360
DOI: 10.2307/2005976
Stable URL: http://www.jstor.org/stable/2005976
Page Count: 24
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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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