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1: 25.10 Zeros
§25.10(i) Distribution
In the region 0 < s < 1 , called the critical strip, ζ ( s ) has infinitely many zeros, distributed symmetrically about the real axis and about the critical line s = 1 2 . … Riemann developed a method for counting the total number N ( T ) of zeros of ζ ( s ) in that portion of the critical strip with 0 < t < T . … Calculations based on the Riemann–Siegel formula reveal that the first ten billion zeros of ζ ( s ) in the critical strip are on the critical line (van de Lune et al. (1986)). More than 41% of all the zeros in the critical strip lie on the critical line (Bui et al. (2011)). …
2: Bibliography V
  • J. van de Lune, H. J. J. te Riele, and D. T. Winter (1986) On the zeros of the Riemann zeta function in the critical strip. IV. Math. Comp. 46 (174), pp. 667–681.
  • 3: 25.18 Methods of Computation
    §25.18(ii) Zeros
    4: 25.15 Dirichlet L -functions
    There are also infinitely many zeros in the critical strip 0 s 1 , located symmetrically about the critical line s = 1 2 , but not necessarily symmetrically about the real axis. …
    5: Errata
  • Subsection 25.10(ii)

    In the paragraph immediately below (25.10.4), it was originally stated that “more than one-third of all zeros in the critical strip lie on the critical line.” which referred to Levinson (1974). This sentence has been updated with “one-third” being replaced with “41%” now referring to Bui et al. (2011) (Suggested by Gergő Nemes on 2021-08-23).