Ax–Katz theorem
E1548926
UNEXPLORED
The Ax–Katz theorem is a result in number theory that gives precise divisibility bounds for the number of solutions to polynomial equations over finite fields, strengthening and refining the Chevalley–Warning theorem.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Ax–Katz theorem canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T22668807 — 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: Ax–Katz theorem Context triple: [Chevalley–Warning theorem, relatedTo, Ax–Katz theorem]
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A.
Szemerédi's theorem
Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
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B.
Green–Tao theorem
The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
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C.
Roth theorem
Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
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D.
Erdős–Turán inequality
The Erdős–Turán inequality is a fundamental result in analytic number theory that provides quantitative bounds on the discrepancy of sequences by relating uniform distribution to exponential sums.
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E.
Gowers inverse theorem in additive combinatorics
The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
- 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: Ax–Katz theorem Target entity description: The Ax–Katz theorem is a result in number theory that gives precise divisibility bounds for the number of solutions to polynomial equations over finite fields, strengthening and refining the Chevalley–Warning theorem.
-
A.
Szemerédi's theorem
Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
-
B.
Green–Tao theorem
The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
-
C.
Roth theorem
Roth's theorem is a fundamental result in Diophantine approximation that gives an essentially optimal bound on how well algebraic irrational numbers can be approximated by rational numbers.
-
D.
Erdős–Turán inequality
The Erdős–Turán inequality is a fundamental result in analytic number theory that provides quantitative bounds on the discrepancy of sequences by relating uniform distribution to exponential sums.
-
E.
Gowers inverse theorem in additive combinatorics
The Gowers inverse theorem in additive combinatorics is a fundamental result that characterizes functions with large Gowers uniformity norms by showing they must correlate with structured objects such as polynomial phase functions, underpinning much of modern higher-order Fourier analysis.
- F. None of above. chosen
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.