On the Zeros of the Riemann Zeta Function

نویسندگان

  • R. P. Brent
  • J. van de Lune
  • H. J. J. te Riele
  • D. T. Winter
  • D. T. WINTER
چکیده

We describe extensive computations which show that Riemann's zeta function f(s) has exactly 200,000,001 zeros of the form a + it in the region 0 < t < 81,702,130.19; all these zeros are simple and he on the line a = j. (This extends a similar result for the first 81,000,001 zeros, established by Brent in Math. Comp., v. 33, 1979, pp. 1361-1372.) Counts of the numbers of Gram blocks of various types and the failures of "Rosser's rule" are given.

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تاریخ انتشار 2010