on critical line or strip
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§25.18(ii) Zeros►Most numerical calculations of the Riemann zeta function are concerned with locating zeros of in an effort to prove or disprove the Riemann hypothesis, which states that all nontrivial zeros of lie on the critical line . Calculations to date (2008) have found no nontrivial zeros off the critical line. …
2: 25.10 Zeros
§25.10(i) Distribution… ►In the region , called the critical strip, has infinitely many zeros, distributed symmetrically about the real axis and about the critical line . … ►Calculations relating to the zeros on the critical line make use of the real-valued function … ►Calculations based on the Riemann–Siegel formula reveal that the first ten billion zeros of 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)). …
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).