On the sign of the difference
Author:
Herman J. J. te Riele
Journal:
Math. Comp. 48 (1987), 323-328
MSC:
Primary 11Y35; Secondary 11M06
DOI:
https://doi.org/10.1090/S0025-5718-1987-0866118-6
MathSciNet review:
866118
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Following a method of Sherman Lehman we show that between and
there are more than
successive integers x for which
. This brings down Sherman Lehman's bound on the smallest number x for which
, namely from
to
. Our result is based on the knowledge of the truth of the Riemann hypothesis for the complex zeros
of the Riemann zeta function which satisfy
, and on the knowledge of the first 15,000 complex zeros to about 28 digits and the next 35,000 to about 14 digits.
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Additional Information
DOI:
https://doi.org/10.1090/S0025-5718-1987-0866118-6
Keywords:
Prime counting function,
approximation,
sign changes,
Riemann hypothesis,
zeros of the Riemann zeta function
Article copyright:
© Copyright 1987
American Mathematical Society