KnowraGeneralized Riemann hypothesisLinked fromLinked fromThe 9 pages that link to Generalized Riemann hypothesis, each with the reason it gives.All 9Broader topic 1Related 1Narrower topic 1Compared with 6Riemann hypothesisBroader topic: It carries the zeta conjecture’s central claim into settings governing primes in arithmetic progressions.Analytic number theoryNarrower topic: It extends the zeta-function zero conjecture to the L-functions used for arithmetic progressions.Prime number theorem for arithmetic progressionsCompared with: It would give stronger error bounds than the unconditional theorem provides.Bombieri–Vinogradov theoremCompared with: The theorem reaches, on average, a range GRH predicts for each fixed modulus.AKS primality testCompared with: Earlier deterministic polynomial-time primality results depended on this unproved hypothesis; AKS does not.Elliott–Halberstam conjectureCompared with: It offers a different route to prime-distribution estimates, but does not simply assert this averaged level.Siegel–Walfisz theoremCompared with: Assuming it gives effective progression estimates over wider modulus ranges than this unconditional theorem.Agrawal's conjectureCompared with: Earlier deterministic polynomial-time primality tests relied on this unproved hypothesis.Artin's conjecture on primitive rootsRelated: Hooley's proof uses it to control primes in the required arithmetic progressions.