E. C. Titchmarsh, The Theory of the Riemann Zeta-Function
E239281
"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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| E. C. Titchmarsh, The Theory of the Riemann Zeta-Function canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2171615 — 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: E. C. Titchmarsh, The Theory of the Riemann Zeta-Function Context triple: [Riemann–Siegel formula, standardReference, E. C. Titchmarsh, The Theory of the Riemann Zeta-Function]
-
A.
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.
-
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.
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.
-
E.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
- 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: E. C. Titchmarsh, The Theory of the Riemann Zeta-Function Target entity description: "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.
-
A.
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.
-
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.
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.
-
E.
An Introduction to the Theory of Numbers
An Introduction to the Theory of Numbers is a classic textbook in number theory, co-authored by G. H. Hardy, that systematically develops fundamental concepts such as divisibility, prime numbers, Diophantine equations, and quadratic forms.
- F. None of above. chosen
Statements (33)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ non-fiction book ⓘ |
| academicDiscipline |
mathematics
ⓘ
number theory ⓘ |
| author | E. C. Titchmarsh ⓘ |
| countryOfPublication | United Kingdom ⓘ |
| describedAs |
authoritative treatment of the Riemann zeta function
ⓘ
classic monograph in analytic number theory ⓘ |
| field | analytic number theory ⓘ |
| genre | mathematics literature ⓘ |
| influenced | research in analytic number theory ⓘ |
| language | English ⓘ |
| mainSubject | Riemann zeta function ⓘ |
| notableFor |
comprehensive coverage of the Riemann zeta function
ⓘ
rigorous analytic methods ⓘ |
| publisher | Oxford University Press ⓘ |
| relatedConcept |
Dirichlet L-functions
ⓘ
L-functions ⓘ |
| relatedWork | H. M. Edwards, Riemann’s Zeta Function ⓘ |
| topic |
Dirichlet series
ⓘ
Euler product ⓘ Riemann hypothesis ⓘ
surface form:
Riemann Hypothesis
analytic continuation ⓘ distribution of primes ⓘ explicit formulae in prime number theory ⓘ functional equation of the Riemann zeta function ⓘ mean values of the zeta function ⓘ prime number theory ⓘ zero-free regions ⓘ zeros of the Riemann zeta function ⓘ |
| usedAs |
graduate-level textbook
ⓘ
reference work for mathematicians ⓘ |
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: E. C. Titchmarsh, The Theory of the Riemann Zeta-Function Description of subject: "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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
Riemann–Siegel formula
→
standardReference
→
E. C. Titchmarsh, The Theory of the Riemann Zeta-Function
ⓘ