Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
E638640
Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
All labels observed (4)
How this entity was disambiguated
This entity first appeared as the object of triple T7030756 — 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: Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan) Context triple: [Multiplicative Number Theory, hasTextbook, Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)]
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A.
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.
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B.
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.
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C.
Selberg–Delange method results
Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
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D.
A. Ivić, The Riemann Zeta-Function
"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.
-
E.
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.
- 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: Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan) Target entity description: Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
-
A.
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.
-
B.
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.
-
C.
Selberg–Delange method results
Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
-
D.
A. Ivić, The Riemann Zeta-Function
"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.
-
E.
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.
- F. None of above. chosen
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
textbook ⓘ |
| academicLevel | graduate ⓘ |
| author |
Hugh L. Montgomery
ⓘ
Robert C. Vaughan ⓘ |
| contribution | systematic exposition of classical multiplicative number theory ⓘ |
| field |
multiplicative number theory
ⓘ
number theory ⓘ |
| focus | classical methods ⓘ |
| genre | mathematics textbook ⓘ |
| hasPart |
development of classical analytic techniques in number theory
ⓘ
treatment of Dirichlet L-functions ⓘ treatment of Dirichlet characters ⓘ treatment of the distribution of primes in arithmetic progressions ⓘ |
| intendedAudience |
graduate students in mathematics
ⓘ
researchers in analytic number theory ⓘ |
| language | English ⓘ |
| subject |
analytic number theory
ⓘ
prime numbers ⓘ |
| topic |
Dirichlet L-functions
ⓘ
Dirichlet characters ⓘ Dirichlet series ⓘ Dirichlet’s theorem on primes in arithmetic progressions ⓘ Euler products ⓘ
linked to:
Euler products for automorphic L-functions
L-functions ⓘ Mertens-type estimates ⓘ Tauberian theorems in number theory ⓘ analytic properties of L-functions ⓘ characters and exponential sums ⓘ characters modulo q ⓘ distribution of prime numbers ⓘ mean values of multiplicative functions ⓘ multiplicative functions ⓘ orthogonality relations of characters ⓘ partial summation and summatory functions ⓘ prime number theorem ⓘ zero-density estimates (classical theory) ⓘ zero-free regions for L-functions ⓘ |
| usedIn |
graduate courses on analytic number theory
ⓘ
graduate courses on multiplicative 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: Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan) Description of subject: Multiplicative Number Theory I. Classical Theory (by Hugh L. Montgomery and Robert C. Vaughan) is a foundational graduate-level textbook that systematically develops the classical theory of multiplicative number theory, including Dirichlet characters, L-functions, and the distribution of prime numbers.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
Multiplicative Number Theory
→
hasTextbook
→
Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
ⓘ
Multiplicative Number Theory
→
hasTextbook
→
Multiplicative Number Theory II. Analytic and Probabilistic Number Theory (Hugh L. Montgomery, Robert C. Vaughan)
ⓘ
linked to: Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
linked to: Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)
Hugh L. Montgomery
→
notableWork
→
Montgomery–Vaughan book "Multiplicative Number Theory I. Classical Theory"
ⓘ
linked to: Multiplicative Number Theory I. Classical Theory (Hugh L. Montgomery, Robert C. Vaughan)