A. Ivić, The Riemann Zeta-Function
E244384
"A. Ivić, The Riemann Zeta-Function" is a comprehensive monograph on the analytic theory of the Riemann zeta function, widely regarded as a standard modern reference in analytic number theory.
All labels observed (3)
| Label | Occurrences |
|---|---|
| A. Ivić, The Riemann Zeta-Function canonical | 1 |
| Ivić, The Riemann Zeta-Function | 1 |
| The Riemann Zeta-Function: Theory and Applications | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2171617 — 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: A. Ivić, The Riemann Zeta-Function Context triple: [Riemann–Siegel formula, standardReference, A. Ivić, The Riemann Zeta-Function]
-
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.
H. M. Edwards, Riemann’s Zeta Function
*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.
-
C.
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.
-
D.
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.
-
E.
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.
- 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: A. Ivić, The Riemann Zeta-Function Target entity description: "A. Ivić, The Riemann Zeta-Function" is a comprehensive monograph on the analytic theory of the Riemann zeta function, widely regarded as a standard modern 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.
H. M. Edwards, Riemann’s Zeta Function
*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.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematics monograph ⓘ reference work ⓘ |
| author | Aleksandar Ivić ⓘ |
| citedIn | research articles in analytic number theory ⓘ |
| classification | mathematics / number theory ⓘ |
| contains | historical notes on the development of the theory of the Riemann zeta function ⓘ |
| countryOfPublication |
United States
ⓘ
linked to:
United States of America
|
| coversTopic |
Dirichlet polynomials
ⓘ
Dirichlet series ⓘ Lindelöf hypothesis (background and consequences) ⓘ
linked to:
Lindelöf hypothesis
Riemann hypothesis (background and consequences) ⓘ approximate functional equations ⓘ distribution of zeros of the Riemann zeta function ⓘ error term in the prime number theorem ⓘ exponential sums in number theory ⓘ functional equation of the Riemann zeta function ⓘ large values of the Riemann zeta function ⓘ mean square of the zeta function on the critical line ⓘ mean values of the Riemann zeta function ⓘ moments of the Riemann zeta function ⓘ small values of the Riemann zeta function ⓘ zero-free regions for the Riemann zeta function ⓘ |
| field | analytic number theory ⓘ |
| focusesOn |
analytic properties of the Riemann zeta function
ⓘ
complex analytic methods in number theory ⓘ |
| hasAbbreviation |
Ivić, The Riemann Zeta-Function
ⓘ
linked to:
A. Ivić, The Riemann Zeta-Function
|
| hasMathematicalReviewNumber | MR0792089 ⓘ |
| hasReputationFor |
comprehensive coverage of analytic theory of the Riemann zeta function
ⓘ
detailed proofs ⓘ extensive bibliography ⓘ |
| intendedAudience |
graduate students in number theory
ⓘ
research mathematicians ⓘ |
| ISBN | 978-0-486-43815-3 ⓘ |
| isWidelyRegardedAs | standard modern reference in analytic number theory ⓘ |
| language | English ⓘ |
| mainSubject | Riemann zeta function ⓘ |
| originalPublisher |
John Wiley & Sons
ⓘ
linked to:
Wiley-Blackwell
|
| pages | 517 ⓘ |
| publicationYear | 1985 ⓘ |
| publisher | Dover Publications ⓘ |
| reprintYear | 2003 ⓘ |
| series | Dover Books on Mathematics ⓘ |
| usedAs | standard reference for results on the Riemann zeta function ⓘ |
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: A. Ivić, The Riemann Zeta-Function Description of subject: "A. Ivić, The Riemann Zeta-Function" is a comprehensive monograph on the analytic theory of the Riemann zeta function, widely regarded as a standard modern reference in analytic number theory.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: A. Ivić, The Riemann Zeta-Function
linked to: A. Ivić, The Riemann Zeta-Function