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An open research record on the Riemann Hypothesis.

NAV READY · TYPE SHORTCUT · ENTER EXECUTES

Critical line

Category
RIEMANN HYPOTHESIS
Definition
The line Re(s)=1/2 at the centre of the critical strip, on which RH predicts every non-trivial zero lies.
Math Level
GENERAL
Index Excerpt
Re(s)=1/2

The critical line is the vertical line Re⁡(s)=1/2\operatorname{Re}(s)=1/2 in the complex plane.

It runs through the middle of the critical strip. The Riemann Hypothesis says that every non-trivial zero of the zeta function lies on this line.

See also: critical strip, real part, non-trivial zero, Riemann Hypothesis..

Related glossary terms

  1. [..]Critical stripGLOSSARY · RIEMANN HYPOTHESIS
  2. [..]Non-trivial zeroGLOSSARY · RIEMANN HYPOTHESIS
  3. [..]Real partGLOSSARY · STANDARD MATHEMATICS
  4. [..]Riemann HypothesisGLOSSARY · RIEMANN HYPOTHESIS

Read this term in context

  1. [..]Who was Bernhard Riemann?ARTICLE · ART-RC-0107
  2. [..]Critical stripARTICLE · ART-RC-0020
  3. [..]Functional equationARTICLE · ART-RC-0022
  4. [..]Non-trivial zeroARTICLE · ART-RC-0019
  5. [..]Real partARTICLE · ART-RC-0015
  6. [..]Riemann HypothesisARTICLE · ART-RC-0006
  7. [..]Zero of a functionARTICLE · ART-RC-0017
  8. [..]What is the Riemann Hypothesis?ARTICLE · ART-RC-0001