GRH
E898459
GRH is a major unproven conjecture in number theory asserting that all nontrivial zeros of a broad class of L-functions lie on a critical line, generalizing the classical Riemann hypothesis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| GRH canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10991079 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: GRH Context triple: [generalized Riemann hypothesis, alsoKnownAs, GRH]
-
A.
GRR
GRR is the IATA airport code for Gerald R. Ford International Airport, the primary commercial airport serving Grand Rapids, Michigan.
-
B.
RGH
RGH is the IATA airport code for Balurghat Airport, a regional airport serving the town of Balurghat in West Bengal, India.
-
C.
GRA
GRA is the ring-shaped orbital motorway encircling Rome, Italy, serving as a major traffic artery for the metropolitan area.
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D.
GANHRI
GANHRI is an international network that brings together and supports national human rights institutions worldwide to promote and protect human rights.
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E.
GHY
GHY is the station code for Guwahati Junction, a major railway hub in the northeastern Indian state of Assam.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: GRH Target entity description: GRH is a major unproven conjecture in number theory asserting that all nontrivial zeros of a broad class of L-functions lie on a critical line, generalizing the classical Riemann hypothesis.
-
A.
GRR
GRR is the IATA airport code for Gerald R. Ford International Airport, the primary commercial airport serving Grand Rapids, Michigan.
-
B.
RGH
RGH is the IATA airport code for Balurghat Airport, a regional airport serving the town of Balurghat in West Bengal, India.
-
C.
GRA
GRA is the ring-shaped orbital motorway encircling Rome, Italy, serving as a major traffic artery for the metropolitan area.
-
D.
GANHRI
GANHRI is an international network that brings together and supports national human rights institutions worldwide to promote and protect human rights.
-
E.
GHY
GHY is the station code for Guwahati Junction, a major railway hub in the northeastern Indian state of Assam.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical conjecture
ⓘ
number theory conjecture ⓘ unproven conjecture ⓘ |
| abbreviationOf | Generalized Riemann Hypothesis NERFINISHED ⓘ |
| appliesTo |
Dirichlet L-functions associated to primitive characters
NERFINISHED
ⓘ
a broad class of L-functions beyond the Riemann zeta function ⓘ |
| asserts | all nontrivial zeros of certain L-functions lie on the critical line Re(s) = 1/2 ⓘ |
| concerns |
Dirichlet L-functions
NERFINISHED
ⓘ
L-functions ⓘ zeros of L-functions ⓘ |
| field |
analytic number theory
ⓘ
number theory ⓘ |
| fullName | Generalized Riemann Hypothesis NERFINISHED ⓘ |
| generalizes | Riemann Hypothesis NERFINISHED ⓘ |
| hasConsequence |
constraints on possible counterexamples to the Riemann Hypothesis
ⓘ
sharper bounds for class numbers of number fields ⓘ |
| hasVariant |
Extended Riemann Hypothesis
NERFINISHED
ⓘ
Grand Riemann Hypothesis NERFINISHED ⓘ |
| implies |
effective versions of the Chebotarev density theorem
ⓘ
improved bounds in computational number theory algorithms ⓘ results on distribution of primes in arithmetic progressions ⓘ results on least quadratic nonresidues ⓘ strong bounds on error terms in prime number theorems for arithmetic progressions ⓘ various bounds in algebraic number theory ⓘ |
| involves |
complex analysis
ⓘ
prime number distribution in arithmetic progressions ⓘ |
| isPartOf | Millennium Prize Problems context ⓘ |
| isStrongerThan | Riemann Hypothesis NERFINISHED ⓘ |
| logicalStatus | independent of current axioms is unknown ⓘ |
| motivation |
generalizing properties of the Riemann zeta function
ⓘ
understanding distribution of primes ⓘ |
| openQuestion | whether any nontrivial zero of Dirichlet L-functions lies off the critical line ⓘ |
| relatedTo |
Dedekind zeta functions
NERFINISHED
ⓘ
Dirichlet characters NERFINISHED ⓘ Riemann Hypothesis NERFINISHED ⓘ automorphic L-functions ⓘ critical line Re(s) = 1/2 ⓘ critical strip 0 < Re(s) < 1 ⓘ zeta functions ⓘ |
| status |
open problem
ⓘ
unproven ⓘ |
| studiedBy | number theorists ⓘ |
| usedIn |
conditional bounds for algorithms in primality testing and factoring
ⓘ
conditional results in algebraic number theory ⓘ conditional results in computational complexity ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: GRH Description of subject: GRH is a major unproven conjecture in number theory asserting that all nontrivial zeros of a broad class of L-functions lie on a critical line, generalizing the classical Riemann hypothesis.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.