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An open research record on the Riemann Hypothesis.

NAV READY · TYPE SHORTCUT · ENTER EXECUTES

Critical strip

Category
RIEMANN HYPOTHESIS
Definition
The region 0 < Re(s) < 1 containing the non-trivial zeros of the Riemann zeta function.
Math Level
GENERAL
Index Excerpt
0 < Re(s) < 1

The critical strip is the region of the complex plane where 0<Re⁡(s)<10<\operatorname{Re}(s)<1.

The non-trivial zeros of the Riemann zeta function lie in this strip. The Riemann Hypothesis makes the much sharper claim that all of them lie on the line running down its middle, Re⁡(s)=1/2\operatorname{Re}(s)=1/2.

See also: complex plane, non-trivial zero, critical line, Riemann Hypothesis..

Related glossary terms

  1. [..]Complex planeGLOSSARY · STANDARD MATHEMATICS
  2. [..]Critical lineGLOSSARY · RIEMANN HYPOTHESIS
  3. [..]Non-trivial zeroGLOSSARY · RIEMANN HYPOTHESIS
  4. [..]Riemann HypothesisGLOSSARY · RIEMANN HYPOTHESIS

Read this term in context

  1. [..]What is analytic continuation?ARTICLE · ART-RC-0116
  2. [..]What is the Riemann xi function?ARTICLE · ART-RC-0114
  3. [..]What is the Riemann zeta function?ARTICLE · ART-RC-0111
  4. [..]Who was Bernhard Riemann?ARTICLE · ART-RC-0107
  5. [..]Analytic continuationARTICLE · ART-RC-0012
  6. [..]Complex planeARTICLE · ART-RC-0014
  7. [..]Critical lineARTICLE · ART-RC-0021
  8. [..]Non-trivial zeroARTICLE · ART-RC-0019
  9. [..]Trivial zeroARTICLE · ART-RC-0018
  10. [..]What is the Riemann Hypothesis?ARTICLE · ART-RC-0001