de Bruijn–Newman constant
E239168
The de Bruijn–Newman constant is a real number arising in the study of the zeros of the Riemann zeta function and related Fourier transforms, central to a refined form of the Riemann Hypothesis.
All labels observed (2)
| Label | Occurrences |
|---|---|
| de Bruijn–Newman constant canonical | 3 |
| de Bruijn–Newman theory | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2169628 — 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: de Bruijn–Newman constant Context triple: [N. G. de Bruijn, notableWork, de Bruijn–Newman constant]
-
A.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
B.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
-
D.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
-
E.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
- 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: de Bruijn–Newman constant Target entity description: The de Bruijn–Newman constant is a real number arising in the study of the zeros of the Riemann zeta function and related Fourier transforms, central to a refined form of the Riemann Hypothesis.
-
A.
Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
-
B.
Riemann–Siegel formula
The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
-
C.
Riemann zeta function
The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
-
D.
Riemann hypothesis
The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
-
E.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
- F. None of above. chosen
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical constant
ⓘ
real number ⓘ |
| appearsIn |
study of deformed Riemann xi functions
ⓘ
theory of entire functions of Laguerre–Pólya class ⓘ |
| characterization | threshold between all-real zeros and some non-real zeros for a family of entire functions ⓘ |
| conjecturedRelationToRiemannHypothesis |
Riemann Hypothesis is equivalent to Λ ≤ 0
ⓘ
linked to:
Riemann hypothesis
|
| conjecturedSign | nonnegative ⓘ |
| connectedTo |
Riemann xi function
ⓘ
distribution of zeros of entire functions ⓘ heat-flow deformation of entire functions ⓘ |
| definitionContext | deformation of the Riemann xi function by the heat equation ⓘ |
| field |
Fourier analysis
ⓘ
analytic number theory ⓘ complex analysis ⓘ |
| furtherDevelopedBy | Charles M. Newman ⓘ |
| hasInequalityFormulation | Λ ≥ 0 ⓘ |
| implication |
if Λ > 0 then some deformations of the xi function have non-real zeros
ⓘ
if Λ ≤ 0 then all zeros of the Riemann xi function are real ⓘ |
| introducedBy |
Nicolaas Govert de Bruijn
ⓘ
linked to:
N. G. de Bruijn
|
| knownLowerBound | Λ ≥ 0 ⓘ |
| knownLowerBoundProvedBy |
Brad Rodgers
ⓘ
Terence Tao ⓘ |
| knownLowerBoundYear | 2018 ⓘ |
| mathematicalDomain | theory of zeta and L-functions ⓘ |
| namedAfter |
Charles M. Newman
ⓘ
Nicolaas Govert de Bruijn ⓘ
linked to:
N. G. de Bruijn
|
| openProblem |
determine the exact value of Λ
ⓘ
prove or disprove Λ = 0 ⓘ |
| property | is the infimum of parameters t for which a deformed xi-function has only real zeros ⓘ |
| refinedConjecture | Λ = 0 ⓘ |
| relatedTo |
Fourier transform
ⓘ
Riemann Hypothesis ⓘ
linked to:
Riemann hypothesis
Riemann zeta function ⓘ entire functions with real zeros ⓘ zeros of the Riemann xi function ⓘ |
| role | measures how far the Riemann Hypothesis could fail ⓘ |
| status |
exact value unknown
ⓘ
sign known to be nonnegative ⓘ |
| symbol | Λ ⓘ |
| upperBound | less than 1 ⓘ |
| usedIn | refined formulations of the Riemann Hypothesis ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: de Bruijn–Newman constant Description of subject: The de Bruijn–Newman constant is a real number arising in the study of the zeros of the Riemann zeta function and related Fourier transforms, central to a refined form of the Riemann Hypothesis.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.