Heilbronn Halberstam
E637295
Heilbronn–Halberstam refers to a result in analytic number theory, associated with Hans Heilbronn and H. Halberstam, concerning the distribution of prime numbers in arithmetic progressions.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Heilbronn Halberstam canonical | 1 |
| Heini Halberstam | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7030667 — 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: Heilbronn Halberstam Context triple: [H. Halberstam, name, Heilbronn Halberstam]
-
A.
Gerhard Weinberg
Gerhard Weinberg is a German-born American historian renowned for his comprehensive scholarship on World War II and the origins and conduct of the Nazi regime.
-
B.
Walter Blum
Walter Blum is a German mathematician known for his contributions to algebra and mathematical education.
-
C.
Charles Schoenbaum
Charles Schoenbaum was an American cinematographer known for his work on numerous Hollywood films during the mid-20th century.
-
D.
Frederick Hollander
Frederick Hollander was a German-born composer and songwriter best known for his film scores and cabaret music, particularly in Hollywood during the 1930s and 1940s.
-
E.
Irving Brecher
Irving Brecher was an American screenwriter best known for his work on Marx Brothers comedies and classic Hollywood films of the 1930s and 1940s.
- 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: Heilbronn Halberstam Target entity description: Heilbronn–Halberstam refers to a result in analytic number theory, associated with Hans Heilbronn and H. Halberstam, concerning the distribution of prime numbers in arithmetic progressions.
-
A.
Gerhard Weinberg
Gerhard Weinberg is a German-born American historian renowned for his comprehensive scholarship on World War II and the origins and conduct of the Nazi regime.
-
B.
Walter Blum
Walter Blum is a German mathematician known for his contributions to algebra and mathematical education.
-
C.
Charles Schoenbaum
Charles Schoenbaum was an American cinematographer known for his work on numerous Hollywood films during the mid-20th century.
-
D.
Frederick Hollander
Frederick Hollander was a German-born composer and songwriter best known for his film scores and cabaret music, particularly in Hollywood during the 1930s and 1940s.
-
E.
Irving Brecher
Irving Brecher was an American screenwriter best known for his work on Marx Brothers comedies and classic Hollywood films of the 1930s and 1940s.
- F. None of above. chosen
Statements (20)
| Predicate | Object |
|---|---|
| instanceOf | theorem in analytic number theory ⓘ |
| approximateDate | 20th century ⓘ |
| area | prime number theory ⓘ |
| concerns |
distribution of prime numbers in arithmetic progressions
ⓘ
primes in arithmetic progressions ⓘ |
| describes | average distribution of primes over moduli ⓘ |
| field | analytic number theory ⓘ |
| hasAuthor |
Hans Heilbronn
NERFINISHED
ⓘ
Hugh Halberstam NERFINISHED ⓘ |
| mathematicalSubjectClassification |
11N13
ⓘ
11N36 ⓘ |
| namedAfter |
Hans Heilbronn
NERFINISHED
ⓘ
Hugh Halberstam NERFINISHED ⓘ |
| relatedTo |
Bombieri–Vinogradov theorem
NERFINISHED
ⓘ
Dirichlet’s theorem on arithmetic progressions NERFINISHED ⓘ generalized Riemann hypothesis NERFINISHED ⓘ |
| topic | distribution of primes in residue classes ⓘ |
| usesConcept |
Dirichlet characters
NERFINISHED
ⓘ
L-functions NERFINISHED ⓘ sieve methods ⓘ |
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: Heilbronn Halberstam Description of subject: Heilbronn–Halberstam refers to a result in analytic number theory, associated with Hans Heilbronn and H. Halberstam, concerning the distribution of prime numbers in arithmetic progressions.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Heini Halberstam