On the zeros of the Riemann zeta function in the critical
70. R. P. Brent, J. van de Lune, H. J. J. te Riele and D. T. Winter,
On the zeros of the Riemann zeta function in the critical strip, II,
Mathematics of Computation 39 (1982), 681-688.
Corrigendum ibid 46 (1986), 771.
We describe extensive computations which show that Riemann's zeta function
has exactly 200,000,001 zeros of the form
sigma + i.t
in the region 0 <t < 81,702,130.19;
all these zeros are simple and lie on the line sigma = 1/2.
This extends a result for the first 81,000,001
zeros, established by Brent in
Counts of the numbers of Gram blocks of various types
and the failures of "Rosser's rule" are given.
A more detailed version appeared as
For a further extension, see
van de Lune et al,
Mathematics of Computation 46 (1986) 667-681.
For more recent results see the
maintained by Sebastian Wedeniwski.
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