Generalized Riemann Hypothesis
- Category
- RIEMANN HYPOTHESIS
- Definition
- A wider family of Riemann-type conjectures about zeros of Dirichlet and related L-functions.
- Math Level
- TECHNICAL
- Index Excerpt
- GRH
The Generalized Riemann Hypothesis, usually abbreviated GRH, extends the Riemann-Hypothesis type of zero-location conjecture to a broader family of -functions.
Many results in number theory and algorithms are known conditionally on GRH. It is related to RH but is a wider and stronger assertion; proving RH alone would not automatically prove every instance of GRH.
See also: Riemann Hypothesis, L-function, conditional theorem..