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Author ID: baker.alan Recent zbMATH articles by "Baker, Alan"
Published as: Baker, A.; Baker, Alan
Homepage: https://www.dpmms.cam.ac.uk/people/ab10005/
External Links: MacTutor · MGP · Wikidata · Math-Net.Ru · GND · IdRef
Awards: Fields Medal (1970)
Documents Indexed: 70 Publications since 1962, including 7 Books
5 Contributions as Editor · 2 Further Contributions
Biographic References: 7 Publications
Co-Authors: 12 Co-Authors with 18 Joint Publications
495 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

63 Publications have been cited 1,297 times in 986 Documents Cited by Year
The equations \(3x^2 - 2 = y^2\) and \(8x^2 - 7 = z^2\). Zbl 0177.06802
Baker, A.; Davenport, Harold
160
1969
Transcendental number theory. Zbl 0297.10013
Baker, Alan
151
1975
Logarithmic forms and group varieties. Zbl 0788.11026
Baker, A.; Wüstholz, G.
97
1993
Linear forms in the logarithms of algebraic numbers. Zbl 0161.05201
Baker, A.
82
1966
Contributions to the theory of diophantine equations. I: On the representation of integers by binary forms. Zbl 0157.09702
Baker, A.
63
1968
Diophantine approximation and Hausdorff dimension. Zbl 0206.05801
Baker, A.; Schmidt, W. M.
58
1970
Transcendental number theory. Paperback ed. Zbl 0715.11032
Baker, Alan
50
1990
Bounds for the solutions of the hyperelliptic equation. Zbl 0174.33803
Baker, A.
49
1969
Linear forms in the logarithmic of algebraic numbers. IV. Zbl 0169.37802
Baker, A.
35
1968
Rational approximations to \(\root 3\of 2\) and other algebraic numbers. Zbl 0222.10036
Baker, A.
34
1964
Logarithmic forms and Diophantine geometry. Zbl 1145.11004
Baker, Alan; Wüstholz, Gisbert
29
2007
On some Diophantine inequalities involving the exponential function. Zbl 0147.30901
Baker, A.
29
1965
On a problem of Chowla. Zbl 0267.10065
Baker, A.; Birch, B. J.; Wirsing, E. A.
26
1973
On some diophantine inequalities involving primes. Zbl 0155.09202
Baker, A.
24
1967
Linear forms in the logarithms of algebraic numbers. III. Zbl 0161.05301
Baker, A.
23
1967
A concise introduction to the theory of numbers. Zbl 0554.10001
Baker, Alan
22
1984
Imaginary quadratic fields with class number 2. Zbl 0219.12008
Baker, A.
22
1971
Continued fractions of transcendental numbers. Zbl 0105.03903
Baker, A.
22
1962
The theory of linear forms in logarithms. Zbl 0361.10028
Baker, A.
21
1977
Linear forms in the logarithms of algebraic numbers. II. Zbl 0161.05202
Baker, A.
20
1967
A sharpening of the bounds for linear forms in logarithms. II. Zbl 0261.10025
Baker, A.
19
1973
Integer points on curves of genus 1. Zbl 0194.07601
Baker, A.; Coates, J.
18
1970
On a fundamental inequality in number theory. Zbl 0219.12009
Baker, A.; Stark, H. M.
17
1971
A sharpening of the bounds for linear forms in logarithms. Zbl 0244.10031
Baker, A.
17
1972
On Mahler’s classification of transcendental numbers. Zbl 0147.03403
Baker, A.
17
1964
Rational approximation to certain algebraic numbers. Zbl 0131.29102
Baker, A.
16
1964
The Diophantine equation \(y^ 2 = ax^ 3 +bx^ 2 +cx+d\). Zbl 0155.08701
Baker, A.
15
1968
Contributions to the theory of diophantine equations. II: The diophantine equation \(y^ 2 = x^ 3 +k\). Zbl 0157.09801
Baker, A.
12
1968
A note on integral integer-valued functions of several variables. Zbl 0189.05101
Baker, A.
10
1967
On a theorem of Sprindzhuk. Zbl 0146.06302
Baker, A.
10
1966
Simultaneous rational approximations to certain algebraic numbers. Zbl 0166.05503
Baker, A.
10
1967
A sharpening of the bounds for linear forms in logarithms. III. Zbl 0301.10030
Baker, A.
9
1975
Approximations to the logarithms of certain rational numbers. Zbl 0201.37603
Baker, A.
8
1964
Transcendental number theory. (Repr. of 1975 with additional material). Zbl 0497.10023
Baker, Alan
8
1979
Fractional parts of powers of rationals. Zbl 0298.10018
Baker, A.; Coates, J.
8
1975
A remark on the class number of quadratic fields. Zbl 0177.07403
Baker, A.
8
1969
On an analogue of Littlewood’s diophantine approximation problem. Zbl 0218.10052
Baker, A.
7
1964
On the periods of the Weierstrass \(\wp\)-function. Zbl 0223.10019
Baker, A.
7
1970
Experiments on the \(abc\)-conjecture. Zbl 1064.11050
Baker, Alan
7
2004
On the quasi-periods of the Weierstrass \(\zeta\)-function. Zbl 0201.05403
Baker, A.
6
1970
An estimate for the \(\wp\)-function at an algebraic point. Zbl 0208.30901
Baker, A.
5
1970
Transcendence theory: advances and applications. Proceedings of a conference held in Cambridge in 1976. Zbl 0357.00010
5
1977
A central theorem in transcendence theory. Zbl 0262.10022
Baker, A.
5
1973
On the least integers represented by the genera of binary quadratic forms. Zbl 0218.10040
Baker, A.; Schinzel, Andrzej
4
1971
Effective methods in diophantine problems. Zbl 0213.05202
Baker, A.
3
1971
Logarithmic forms and the \(abc\)-conjecture. Zbl 0973.11047
Baker, A.
3
1998
A comprehensive course in number theory. Zbl 1254.11001
Baker, Alan
3
2012
New advances in transcendence theory. (Proceedings of a Symposium, University of Durham, UK, July 1986). Zbl 0644.00005
3
1988
On effective approximations to cubic irrationals. Zbl 0656.10025
Baker, A.; Stewart, C. L.
2
1988
On the class number of imaginary quadratic fields. Zbl 0221.12006
Baker, A.
2
1971
On a fundamental inequality in number theory. Zbl 0239.12003
Baker, A.; Stark, H. M.
2
1972
On an arithmetical function associated with the \(abc\)-conjecture. Zbl 1204.11155
Baker, Alan
2
2007
Number theory, transcendence and Diophantine geometry in the next millennium. Zbl 0960.11001
Baker, A.; Wüstholz, G.
2
2000
Effective methods in the theory of numbers. Zbl 0222.10001
Baker, A.
1
1971
Recent advances in transcendence theory. Zbl 0291.10027
Baker, A.
1
1973
Some historical remarks on number theory. Zbl 0333.01001
Baker, Alan
1
1975
Further aspects of transcendence theory. Zbl 0343.10016
Baker, A.; Stewart, C. L.
1
1977
Squaring the circle: Transcendence, logarithmic forms and diophantine analysis. Zbl 0856.11002
Baker, A.
1
1996
Mathematics and explanatory generality. Zbl 1420.00018
Baker, Alan
1
2017
A tribute to Paul Erdős. Zbl 0706.00007
1
1990
The evolution of transcendence theory. Zbl 0761.11031
Baker, A.
1
1991
Power series representing algebraic functions. Zbl 0136.34101
Baker, A.
1
1965
On Mahler’s classification of transcendental numbers. II: Simultaneous Diophantine approximation. Zbl 0148.27701
Baker, A.
1
1967
Mathematics and explanatory generality. Zbl 1420.00018
Baker, Alan
1
2017
A comprehensive course in number theory. Zbl 1254.11001
Baker, Alan
3
2012
Logarithmic forms and Diophantine geometry. Zbl 1145.11004
Baker, Alan; Wüstholz, Gisbert
29
2007
On an arithmetical function associated with the \(abc\)-conjecture. Zbl 1204.11155
Baker, Alan
2
2007
Experiments on the \(abc\)-conjecture. Zbl 1064.11050
Baker, Alan
7
2004
Number theory, transcendence and Diophantine geometry in the next millennium. Zbl 0960.11001
Baker, A.; Wüstholz, G.
2
2000
Logarithmic forms and the \(abc\)-conjecture. Zbl 0973.11047
Baker, A.
3
1998
Squaring the circle: Transcendence, logarithmic forms and diophantine analysis. Zbl 0856.11002
Baker, A.
1
1996
Logarithmic forms and group varieties. Zbl 0788.11026
Baker, A.; Wüstholz, G.
97
1993
The evolution of transcendence theory. Zbl 0761.11031
Baker, A.
1
1991
Transcendental number theory. Paperback ed. Zbl 0715.11032
Baker, Alan
50
1990
A tribute to Paul Erdős. Zbl 0706.00007
1
1990
New advances in transcendence theory. (Proceedings of a Symposium, University of Durham, UK, July 1986). Zbl 0644.00005
3
1988
On effective approximations to cubic irrationals. Zbl 0656.10025
Baker, A.; Stewart, C. L.
2
1988
A concise introduction to the theory of numbers. Zbl 0554.10001
Baker, Alan
22
1984
Transcendental number theory. (Repr. of 1975 with additional material). Zbl 0497.10023
Baker, Alan
8
1979
The theory of linear forms in logarithms. Zbl 0361.10028
Baker, A.
21
1977
Transcendence theory: advances and applications. Proceedings of a conference held in Cambridge in 1976. Zbl 0357.00010
5
1977
Further aspects of transcendence theory. Zbl 0343.10016
Baker, A.; Stewart, C. L.
1
1977
Transcendental number theory. Zbl 0297.10013
Baker, Alan
151
1975
A sharpening of the bounds for linear forms in logarithms. III. Zbl 0301.10030
Baker, A.
9
1975
Fractional parts of powers of rationals. Zbl 0298.10018
Baker, A.; Coates, J.
8
1975
Some historical remarks on number theory. Zbl 0333.01001
Baker, Alan
1
1975
On a problem of Chowla. Zbl 0267.10065
Baker, A.; Birch, B. J.; Wirsing, E. A.
26
1973
A sharpening of the bounds for linear forms in logarithms. II. Zbl 0261.10025
Baker, A.
19
1973
A central theorem in transcendence theory. Zbl 0262.10022
Baker, A.
5
1973
Recent advances in transcendence theory. Zbl 0291.10027
Baker, A.
1
1973
A sharpening of the bounds for linear forms in logarithms. Zbl 0244.10031
Baker, A.
17
1972
On a fundamental inequality in number theory. Zbl 0239.12003
Baker, A.; Stark, H. M.
2
1972
Imaginary quadratic fields with class number 2. Zbl 0219.12008
Baker, A.
22
1971
On a fundamental inequality in number theory. Zbl 0219.12009
Baker, A.; Stark, H. M.
17
1971
On the least integers represented by the genera of binary quadratic forms. Zbl 0218.10040
Baker, A.; Schinzel, Andrzej
4
1971
Effective methods in diophantine problems. Zbl 0213.05202
Baker, A.
3
1971
On the class number of imaginary quadratic fields. Zbl 0221.12006
Baker, A.
2
1971
Effective methods in the theory of numbers. Zbl 0222.10001
Baker, A.
1
1971
Diophantine approximation and Hausdorff dimension. Zbl 0206.05801
Baker, A.; Schmidt, W. M.
58
1970
Integer points on curves of genus 1. Zbl 0194.07601
Baker, A.; Coates, J.
18
1970
On the periods of the Weierstrass \(\wp\)-function. Zbl 0223.10019
Baker, A.
7
1970
On the quasi-periods of the Weierstrass \(\zeta\)-function. Zbl 0201.05403
Baker, A.
6
1970
An estimate for the \(\wp\)-function at an algebraic point. Zbl 0208.30901
Baker, A.
5
1970
The equations \(3x^2 - 2 = y^2\) and \(8x^2 - 7 = z^2\). Zbl 0177.06802
Baker, A.; Davenport, Harold
160
1969
Bounds for the solutions of the hyperelliptic equation. Zbl 0174.33803
Baker, A.
49
1969
A remark on the class number of quadratic fields. Zbl 0177.07403
Baker, A.
8
1969
Contributions to the theory of diophantine equations. I: On the representation of integers by binary forms. Zbl 0157.09702
Baker, A.
63
1968
Linear forms in the logarithmic of algebraic numbers. IV. Zbl 0169.37802
Baker, A.
35
1968
The Diophantine equation \(y^ 2 = ax^ 3 +bx^ 2 +cx+d\). Zbl 0155.08701
Baker, A.
15
1968
Contributions to the theory of diophantine equations. II: The diophantine equation \(y^ 2 = x^ 3 +k\). Zbl 0157.09801
Baker, A.
12
1968
On some diophantine inequalities involving primes. Zbl 0155.09202
Baker, A.
24
1967
Linear forms in the logarithms of algebraic numbers. III. Zbl 0161.05301
Baker, A.
23
1967
Linear forms in the logarithms of algebraic numbers. II. Zbl 0161.05202
Baker, A.
20
1967
A note on integral integer-valued functions of several variables. Zbl 0189.05101
Baker, A.
10
1967
Simultaneous rational approximations to certain algebraic numbers. Zbl 0166.05503
Baker, A.
10
1967
On Mahler’s classification of transcendental numbers. II: Simultaneous Diophantine approximation. Zbl 0148.27701
Baker, A.
1
1967
Linear forms in the logarithms of algebraic numbers. Zbl 0161.05201
Baker, A.
82
1966
On a theorem of Sprindzhuk. Zbl 0146.06302
Baker, A.
10
1966
On some Diophantine inequalities involving the exponential function. Zbl 0147.30901
Baker, A.
29
1965
Power series representing algebraic functions. Zbl 0136.34101
Baker, A.
1
1965
Rational approximations to \(\root 3\of 2\) and other algebraic numbers. Zbl 0222.10036
Baker, A.
34
1964
On Mahler’s classification of transcendental numbers. Zbl 0147.03403
Baker, A.
17
1964
Rational approximation to certain algebraic numbers. Zbl 0131.29102
Baker, A.
16
1964
Approximations to the logarithms of certain rational numbers. Zbl 0201.37603
Baker, A.
8
1964
On an analogue of Littlewood’s diophantine approximation problem. Zbl 0218.10052
Baker, A.
7
1964
Continued fractions of transcendental numbers. Zbl 0105.03903
Baker, A.
22
1962
all top 5

Cited by 917 Authors

31 Luca, Florian
28 Togbé, Alain
22 Bugeaud, Yann
22 Dujella, Andrej
19 Ziegler, Volker
18 Murty, Maruti Ram
15 Gaál, István
13 Mignotte, Maurice
13 Pethő, Attila
13 Shorey, Tarlok Nath
12 Bennett, Michael A.
12 Fujita, Yasutsugu Fujita
12 Stewart, Cameron L.
11 Fuchs, Clemens
11 He, Bo
11 Waldschmidt, Michel
10 Pintér, Ákos
9 Bravo, Jhon Jairo
9 de Weger, Benjamin M. M.
9 Erduvan, Fatih
9 Filipin, Alan
9 Győry, Kálmán
9 Keskin, Refik
9 Tijdeman, Robert
8 Bernik, Vasiliĭ Ivanovich
8 Cipu, Mihai
8 Liu, Ming-Chit
8 Rihane, Salah Eddine
8 Yu, Kunrui
7 Adamczewski, Boris
7 Ddamulira, Mahadi
7 Gómez, Carlos Alexis
7 Jadrijević, Borka
7 Matala-aho, Tapani
7 Saradha, N.
6 Baker, Roger C.
6 Bombieri, Enrico
6 Kaliada, Dzianis
6 Murty, Vijaya Kumar
6 Tengely, Szabolcs
6 Tichy, Robert Franz
6 Wüstholz, Gisbert
6 Zannier, Umberto M.
5 Budarina, Natalia Viktorovna
5 Chatterjee, Tapas
5 Girstmair, Kurt
5 Gun, Sanoli
5 Hajdu, Lajos
5 Hussain, Mumtaz
5 Kovács, Tünde
5 Lang, Serge
5 Pohst, Michael E.
5 Roy, Damien
5 Şiar, Zafer
5 Tzanakis, Nikos
5 van der Poorten, Alfred J.
5 Wang, Baowei
4 Baker, Alan
4 Bharadwaj, Abhishek T.
4 Bosser, Vincent
4 Brindza, Béla
4 Chang, Chieh-Yu
4 Coman, Dan
4 Dodson, Michael Maurice
4 Dubickas, Artūras
4 Evertse, Jan-Hendrik
4 Fel’dman, Naum Il’ich
4 Hernández Hernández, Santos
4 Herrera, José L.
4 Heuberger, Clemens
4 Hirata-Kohno, Noriko
4 Lapidus, Michel L.
4 Masser, David William
4 Petričević, Vinko
4 Poletsky, Evgeny A.
4 Poulakis, Dimitrios
4 Saha, Ekata
4 Schmidt, Wolfgang M.
4 Shmelev, Andrey A.
4 Väänänen, Keijo O.
4 Xu, Ming
3 Albu, Toma
3 Bérczes, Attila
3 Bertrand, Daniel
3 Bundschuh, Peter
3 Chim, Kwok Chi
3 Coates, John H.
3 Dhillon, Sonika
3 Durand, Arnaud
3 Franušić, Zrinka
3 Fujii, Akio
3 García Lomelí, Ana Cecilia
3 Gaudron, Éric
3 Glass, Andrew M. W.
3 Goldfeld, Dorian Morris
3 Goldstein, Larry Joel
3 Götze, Friedrich
3 Hbaib, Mohamed
3 Hessami Pilehrood, Tatiana
3 Lagarias, Jeffrey C.
...and 817 more Authors
all top 5

Cited in 216 Serials

115 Journal of Number Theory
33 Transactions of the American Mathematical Society
32 Mathematical Notes
31 Journal de Théorie des Nombres de Bordeaux
29 Mathematics of Computation
24 Compositio Mathematica
24 International Journal of Number Theory
20 Mathematical Proceedings of the Cambridge Philosophical Society
19 Rocky Mountain Journal of Mathematics
19 Proceedings of the American Mathematical Society
17 Monatshefte für Mathematik
17 Indagationes Mathematicae. New Series
16 Mathematische Annalen
16 The Ramanujan Journal
15 Periodica Mathematica Hungarica
14 Archiv der Mathematik
14 Acta Mathematica Hungarica
13 Acta Arithmetica
13 Inventiones Mathematicae
13 Mathematika
12 Proceedings of the Japan Academy. Series A
11 Journal of Symbolic Computation
10 Bulletin of the Australian Mathematical Society
9 Glasgow Mathematical Journal
9 Mathematische Zeitschrift
9 Theoretical Computer Science
9 Boletín de la Sociedad Matemática Mexicana. Third Series
8 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
8 Duke Mathematical Journal
8 Functiones et Approximatio. Commentarii Mathematici
7 Lithuanian Mathematical Journal
7 Bulletin of the American Mathematical Society
7 Chebyshevskiĭ Sbornik
6 Journal of Mathematical Analysis and Applications
6 Annales de l’Institut Fourier
6 Journal of Algebra
6 Glasnik Matematički. Serija III
6 Science China. Mathematics
5 Acta Mathematica
5 Advances in Mathematics
5 Bulletin de la Société Mathématique de France
5 Journal für die Reine und Angewandte Mathematik
5 Manuscripta Mathematica
5 Acta Mathematica et Informatica Universitatis Ostraviensis
5 Journal of Integer Sequences
5 Trudy Instituta Matematiki
5 Integers
4 Indian Journal of Pure & Applied Mathematics
4 Israel Journal of Mathematics
4 Journal d’Analyse Mathématique
4 Journal of Soviet Mathematics
4 The Journal of Symbolic Logic
4 Mathematica Slovaca
4 Results in Mathematics
4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
4 Journal of the European Mathematical Society (JEMS)
4 Bulletin of the Brazilian Mathematical Society. New Series
4 Proceedings of the Steklov Institute of Mathematics
4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
4 Research in Number Theory
3 Acta Mathematica Academiae Scientiarum Hungaricae
3 Archive for History of Exact Sciences
3 The Mathematical Intelligencer
3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
3 Czechoslovak Mathematical Journal
3 Journal of Combinatorial Theory. Series A
3 Journal of Functional Analysis
3 Michigan Mathematical Journal
3 Nagoya Mathematical Journal
3 Constructive Approximation
3 Bulletin of the American Mathematical Society. New Series
3 Mémoires de la Société Mathématique de France. Nouvelle Série
3 Expositiones Mathematicae
3 Experimental Mathematics
3 LMS Journal of Computation and Mathematics
3 Advances in Difference Equations
3 Afrika Matematika
2 Analysis Mathematica
2 Discrete Applied Mathematics
2 Discrete Mathematics
2 Information Processing Letters
2 Journal of Geometry and Physics
2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
2 Annali di Matematica Pura ed Applicata. Serie Quarta
2 Bulletin of the London Mathematical Society
2 Canadian Mathematical Bulletin
2 Illinois Journal of Mathematics
2 Journal of Combinatorial Theory. Series B
2 Journal of Differential Equations
2 Journal of the Korean Mathematical Society
2 Proceedings of the Edinburgh Mathematical Society. Series II
2 Quaestiones Mathematicae
2 Rendiconti del Circolo Matemàtico di Palermo. Serie II
2 Rendiconti del Seminario Matematico della Università di Padova
2 European Journal of Combinatorics
2 Physica D
2 Graphs and Combinatorics
2 Journal of Complexity
2 Information and Computation
2 Journal of the American Mathematical Society
...and 116 more Serials
all top 5

Cited in 50 Fields

845 Number theory (11-XX)
73 Algebraic geometry (14-XX)
44 Computer science (68-XX)
34 Dynamical systems and ergodic theory (37-XX)
29 Mathematical logic and foundations (03-XX)
26 Functions of a complex variable (30-XX)
25 Measure and integration (28-XX)
21 Special functions (33-XX)
20 Field theory and polynomials (12-XX)
19 Combinatorics (05-XX)
17 Approximations and expansions (41-XX)
16 Group theory and generalizations (20-XX)
15 Several complex variables and analytic spaces (32-XX)
12 Probability theory and stochastic processes (60-XX)
11 Harmonic analysis on Euclidean spaces (42-XX)
10 History and biography (01-XX)
9 Partial differential equations (35-XX)
9 Numerical analysis (65-XX)
8 Manifolds and cell complexes (57-XX)
7 Commutative algebra (13-XX)
7 Information and communication theory, circuits (94-XX)
6 Associative rings and algebras (16-XX)
6 Topological groups, Lie groups (22-XX)
6 Operator theory (47-XX)
6 Differential geometry (53-XX)
5 General and overarching topics; collections (00-XX)
5 Operations research, mathematical programming (90-XX)
4 Difference and functional equations (39-XX)
4 Sequences, series, summability (40-XX)
4 Functional analysis (46-XX)
4 Geometry (51-XX)
4 Convex and discrete geometry (52-XX)
4 Quantum theory (81-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Ordinary differential equations (34-XX)
3 Global analysis, analysis on manifolds (58-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
3 Systems theory; control (93-XX)
2 Order, lattices, ordered algebraic structures (06-XX)
2 Potential theory (31-XX)
2 General topology (54-XX)
2 Statistics (62-XX)
1 Category theory; homological algebra (18-XX)
1 Real functions (26-XX)
1 Integral transforms, operational calculus (44-XX)
1 Mechanics of particles and systems (70-XX)
1 Mechanics of deformable solids (74-XX)
1 Fluid mechanics (76-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Relativity and gravitational theory (83-XX)

Citations by Year

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