critical strip

The critical stripMathworldPlanetmath of the Riemann zeta functionDlmfDlmfMathworldPlanetmath is {s:0Re(s)1}. The zeroes of the Riemann zeta function outside of the critical strip are exactly the set of all negative even integers. The location of the zeroes of the Riemann zeta function inside the critical strip is not totally known; about these zeroes is crucial in analytic number theoryMathworldPlanetmath and the of primes. The Riemann hypothesis asserts that all zeroes of the Riemann zeta function that are in the critical strip lie on the line Re(s)=12. This is all explained in more detail in the entry Riemann zeta function (

It is well known that no zeroes of the Riemann zeta function lie on either of the lines Re(s)=0 and Re(s)=1. (See this entry ( for a proof.) Therefore, some people use the “critical strip” to refer to the region ( {s:0<Re(s)<1}. (Note that this is the interior of the critical strip as defined above.) For example, this usage in the title of the entry formulae for zeta in the critical strip.

Title critical strip
Canonical name CriticalStrip
Date of creation 2013-03-22 16:07:21
Last modified on 2013-03-22 16:07:21
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 11
Author Wkbj79 (1863)
Entry type Definition
Classification msc 11M06
Related topic FormulaeForZetaInTheCriticalStrip
Related topic ValueOfTheRiemannZetaFunctionAtS0
Related topic AnalyticContinuationOfRiemannZeta