Transcendental Number Theory
E772535
Transcendental Number Theory is a mathematical monograph by Alan Baker that develops methods for studying transcendental and algebraic numbers, particularly through linear forms in logarithms.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Transcendental Number Theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T9030830 — 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: Transcendental Number Theory Context triple: [Alan Baker, notablePublication, Transcendental Number Theory]
-
A.
An Introduction to Diophantine Approximation
"An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
-
B.
Diophantine approximation
Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
-
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.
Liouville numbers
Liouville numbers are real numbers that can be approximated extremely closely by rationals, making them a classic example of transcendental numbers in number theory.
-
E.
Baker theorem on linear forms in logarithms
The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
- 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: Transcendental Number Theory Target entity description: Transcendental Number Theory is a mathematical monograph by Alan Baker that develops methods for studying transcendental and algebraic numbers, particularly through linear forms in logarithms.
-
A.
An Introduction to Diophantine Approximation
"An Introduction to Diophantine Approximation" is a classic mathematical monograph that systematically develops the theory of approximating real numbers by rationals, aimed at advanced undergraduates and researchers in number theory.
-
B.
Diophantine approximation
Diophantine approximation is a branch of number theory that studies how closely real numbers can be approximated by rational numbers, often with quantitative bounds on the quality of approximation.
-
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.
Liouville numbers
Liouville numbers are real numbers that can be approximated extremely closely by rationals, making them a classic example of transcendental numbers in number theory.
-
E.
Baker theorem on linear forms in logarithms
The Baker theorem on linear forms in logarithms is a fundamental result in transcendental number theory that provides explicit lower bounds for nonzero linear combinations of logarithms of algebraic numbers, with powerful applications to Diophantine equations and Diophantine approximation.
- F. None of above. chosen
Statements (42)
| Predicate | Object |
|---|---|
| instanceOf |
book
ⓘ
mathematical monograph ⓘ |
| author | Alan Baker ⓘ |
| countryOfPublication | United Kingdom ⓘ |
| field |
number theory
ⓘ
transcendental number theory ⓘ |
| focusesOn |
Baker’s theory of linear forms in logarithms
ⓘ
Diophantine approximation ⓘ applications to Diophantine equations ⓘ effective results in transcendence theory ⓘ lower bounds for linear forms in logarithms ⓘ |
| hasAudience |
graduate students in mathematics
ⓘ
researchers in number theory ⓘ |
| hasAuthorNationality | British ⓘ |
| hasTopic |
Baker-type bounds
ⓘ
algebraic independence ⓘ applications to exponential Diophantine equations ⓘ auxiliary functions in transcendence theory ⓘ estimates for logarithmic forms ⓘ heights of algebraic numbers ⓘ linear forms in complex logarithms ⓘ p-adic linear forms in logarithms ⓘ transcendence proofs ⓘ |
| influenced |
development of effective Diophantine methods
ⓘ
later research in transcendental number theory ⓘ |
| influencedBy |
Gelfond–Schneider theorem
ⓘ
work of Aleksandr Gelfond ⓘ work of Theodor Schneider ⓘ |
| language | English ⓘ |
| mainSubject |
algebraic numbers
ⓘ
linear forms in logarithms ⓘ transcendental numbers ⓘ |
| notableFor |
influencing proofs of finiteness results for Diophantine equations
ⓘ
providing effective bounds in transcendence problems ⓘ systematic development of linear forms in logarithms ⓘ |
| publicationYear | 1975 ⓘ |
| publisher | Cambridge University Press ⓘ |
| relatedTo |
Diophantine equations
ⓘ
algebraic number theory ⓘ analytic number theory ⓘ |
| relatedWork | A. Baker’s papers on linear forms in logarithms ⓘ |
| series | Cambridge Tracts in Mathematics ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Transcendental Number Theory Description of subject: Transcendental Number Theory is a mathematical monograph by Alan Baker that develops methods for studying transcendental and algebraic numbers, particularly through linear forms in logarithms.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.