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Critical Strip


CriticalStrip

The region 0<sigma<1, where sigma is defined as the real part of a complex number s=sigma+it. All nontrivial zeros (i.e., those not at negative even integers) of the Riemann zeta function lie inside this strip.


See also

Critical Line, Riemann Hypothesis, Riemann Zeta Function, Riemann Zeta Function Zeros

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References

Brent, R. P. "On the Zeros of the Riemann Zeta Function in the Critical Strip." Math. Comput. 33, 1361-1372, 1979.Brent, R. P.; van de Lune, J.; te Riele, H. J. J.; and Winter, D. T. "On the Zeros of the Riemann Zeta Function in the Critical Strip. II." Math. Comput. 39, 681-688, 1982.Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 195, 2003.

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Critical Strip

Cite this as:

Weisstein, Eric W. "Critical Strip." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CriticalStrip.html

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