H. M. Edwards, Riemann’s Zeta Function
E241727
*H. M. Edwards, Riemann’s Zeta Function* is a classic monograph that provides a rigorous, historically informed, and comprehensive study of the Riemann zeta function and the Riemann Hypothesis, widely regarded as a standard reference in analytic number theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| H. M. Edwards, Riemann’s Zeta Function canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T2171616 — 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: H. M. Edwards, Riemann’s Zeta Function Context triple: [Riemann–Siegel formula, standardReference, H. M. Edwards, Riemann’s Zeta Function]
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A.
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function
"E. C. Titchmarsh, The Theory of the Riemann Zeta-Function" is a classic monograph in analytic number theory that provides a comprehensive and authoritative treatment of the Riemann zeta function and related topics.
-
B.
Euler product formula for the Riemann zeta function
The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
-
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–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.
-
E.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
- 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: H. M. Edwards, Riemann’s Zeta Function Target entity description: *H. M. Edwards, Riemann’s Zeta Function* is a classic monograph that provides a rigorous, historically informed, and comprehensive study of the Riemann zeta function and the Riemann Hypothesis, widely regarded as a standard reference in analytic number theory.
-
A.
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function
"E. C. Titchmarsh, The Theory of the Riemann Zeta-Function" is a classic monograph in analytic number theory that provides a comprehensive and authoritative treatment of the Riemann zeta function and related topics.
-
B.
Euler product formula for the Riemann zeta function
The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
-
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–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.
-
E.
Multiplicative Number Theory
Multiplicative Number Theory is a branch of analytic number theory that studies arithmetic functions and prime number distributions through their multiplicative properties and associated Dirichlet series.
- F. None of above. chosen
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ number theory book ⓘ |
| author |
H. M. Edwards
ⓘ
Harold M. Edwards ⓘ |
| countryOfPublication |
United States of America
ⓘ
surface form:
United States
|
| covers |
Dirichlet series
ⓘ
Euler product formula for the Riemann zeta function ⓘ
surface form:
Euler product
Hadamard product for the zeta function ⓘ critical line of the Riemann zeta function ⓘ critical strip of the Riemann zeta function ⓘ entire function theory related to zeta ⓘ prime number theorem (classical aspects) ⓘ |
| emphasizes |
Riemann’s original methods
ⓘ
historical development of the theory ⓘ |
| field | analytic number theory ⓘ |
| focusesOn |
Riemann’s original 1859 memoir
ⓘ
analytic continuation of the Riemann zeta function ⓘ distribution of zeros of the Riemann zeta function ⓘ functional equation of the Riemann zeta function ⓘ |
| hasFormat | print ⓘ |
| hasReputation |
comprehensive coverage of classical results
ⓘ
historically oriented treatment of Riemann’s work ⓘ rigorous exposition ⓘ |
| hasSubjectCategory |
Complex analysis
ⓘ
Mathematics ⓘ Number theory ⓘ |
| includes |
detailed proofs of classical theorems about zeta
ⓘ
discussion of the explicit formula relating primes and zeros ⓘ discussion of the zeros of the zeta function ⓘ |
| isConsidered |
classic monograph in analytic number theory
ⓘ
standard reference on the Riemann Hypothesis ⓘ standard reference on the Riemann zeta function ⓘ |
| isUsedAs |
reference text for research on the Riemann zeta function
ⓘ
reference text in courses on analytic number theory ⓘ |
| language | English ⓘ |
| mainSubject |
Riemann hypothesis
ⓘ
surface form:
Riemann Hypothesis
Riemann zeta function ⓘ |
| provides |
comprehensive study of the Riemann zeta function
ⓘ
historically informed exposition of the Riemann zeta function ⓘ rigorous treatment of the Riemann zeta function ⓘ |
| publicationYear | 1974 ⓘ |
| publisher | Academic Press ⓘ |
| targetAudience |
graduate students in mathematics
ⓘ
researchers in analytic number theory ⓘ |
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: H. M. Edwards, Riemann’s Zeta Function Description of subject: *H. M. Edwards, Riemann’s Zeta Function* is a classic monograph that provides a rigorous, historically informed, and comprehensive study of the Riemann zeta function and the Riemann Hypothesis, widely regarded as a standard reference in analytic number theory.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function
→
relatedWork
→
H. M. Edwards, Riemann’s Zeta Function
ⓘ