# critical strip

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## 5 matching pages

##### 1: 25.10 Zeros

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###### §25.10(i) Distribution

… ►In the region $$, called the*critical strip*, $\zeta \left(s\right)$ has infinitely many zeros, distributed symmetrically about the real axis and about the*critical line*$\mathrm{\Re}s=\frac{1}{2}$. … ►Riemann developed a method for counting the total number $N(T)$ of zeros of $\zeta \left(s\right)$ in that portion of the critical strip with $$. … ►Calculations based on the Riemann–Siegel formula reveal that the first ten billion zeros of $\zeta \left(s\right)$ 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

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On the zeros of the Riemann zeta function in the critical strip. IV.
Math. Comp. 46 (174), pp. 667–681.
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##### 3: 25.18 Methods of Computation

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###### §25.18(ii) Zeros

…##### 4: 25.15 Dirichlet $L$-functions

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►There are also infinitely many zeros in the critical strip
$0\le \mathrm{\Re}s\le 1$, located symmetrically about the critical line $\mathrm{\Re}s=\frac{1}{2}$, but not necessarily symmetrically about the real axis.
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##### 5: Errata

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Subsection 25.10(ii)
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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*).