×
Author ID: birch.bryan-j Recent zbMATH articles by "Birch, Bryan John"
Published as: Birch, B. J.; Birch, Bryan; Birch, B.; Birch, Bryan J.
Homepage: https://www.maths.ox.ac.uk/people/bryan.birch
External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef

Publications by Year

Citations contained in zbMATH Open

59 Publications have been cited 1,016 times in 890 Documents Cited by Year
Forms in many variables. Zbl 0103.03102
Birch, B. J.
117
1962
Notes on elliptic curves. II. Zbl 0147.02506
Birch, B. J.; Swinnerton-Dyer, H. P. F.
116
1965
How the number of points of an elliptic curve over a fixed prime field varies. Zbl 0183.25503
Birch, B. J.
71
1968
Global class field theory. Zbl 1179.11041
Tate, J. T.
67
1967
Notes on elliptic curves. I. Zbl 0118.27601
Birch, B. J.; Swinnerton-Dyer, H. P. F.
65
1963
Incomplete Kloosterman sums and a divisor problem. Appendix: On some exponential sums by Bryan J. Birch and Enrico Bombieri. Zbl 0572.10029
Friedlander, John B.; Iwaniec, Henryk
59
1985
Modular functions of one variable. IV. Proceedings of the international summer school, University of Antwerp, RUCA, July 17 – August 3, 1972. Zbl 0315.14014
58
1975
The parity of the rank of the Mordell-Weil group. Zbl 0146.42401
Birch, B. J.; Stephens, N. M.
42
1966
On a problem of Chowla. Zbl 0267.10065
Baker, A.; Birch, B. J.; Wirsing, E. A.
34
1973
Homogeneous forms of odd degree in a large number of variables. Zbl 0081.04501
Birch, B. J.
33
1957
Finiteness theorems for binary forms with given discriminant. Zbl 0248.12002
Birch, B. J.; Merriman, J. R.
31
1972
Weber’s class invariants. Zbl 0226.12005
Birch, B. J.
30
1969
Note on a problem of Chowla. Zbl 0091.04301
Birch, B. J.; Swinnerton-Dyer, H. P. F.
28
1959
Elliptic curves and modular functions. Zbl 1214.11081
Swinnerton-Dyer, H. P. F.; Birch, B. J.
24
1975
A look back at Ramanujan’s notebooks. Zbl 0305.10002
Birch, B. J.
22
1975
On 3 \(N\) points in a plane. Zbl 0089.38502
Birch, B. J.
21
1959
Noncongruence subgroups, covers and drawings. Zbl 0930.11024
Birch, Bryan
20
1994
Note on a problem of Erdős. Zbl 0093.05003
Birch, B. J.
18
1959
The Hasse problem for rational surfaces. Zbl 0326.14007
Birch, B. J.; Swinnterton-Dyer, H. P. F.
16
1974
Cyclotomic fields and Kummer extensions. Zbl 1492.11155
Birch, B. J.
15
1967
On the inhomogeneous minimum of the product of n linear forms. Zbl 0074.03702
Birch, B. J.; Swinnerton-Dyer, H. P. F.
14
1956
On the orbit-sizes of permutation groups containing elements separating finite subsets. Zbl 0334.20003
Birch, B. J.; Burns, R. G.; Macdonald, Sheila Oates; Neumann, Peter M.
13
1976
Simultaneous quadratic forms. Zbl 0111.02001
Birch, B. J.; Lewis, D. J.; Murphy, T. G.
13
1962
Heegner points of elliptic curves. Zbl 0317.14015
Birch, B. J.
12
1975
Quadratic equations in several variables. Zbl 0081.04401
Birch, B. J.; Davenport, Harold
12
1958
On a theorem of Davenport and Heilbronn. Zbl 0082.26002
Birch, B. J.; Davenport, Harold
12
1958
On the difference \(x^ 3 -y^ 2\). Zbl 0144.03901
Birch, B. J.; Chowla, Sarvadaman; Hall, M. jun.; Schinzel, Andrzej
12
1965
Complex multiplication. Zbl 1492.11104
Serre, J.-P.
12
1967
Waring’s problem in algebraic number fields. Zbl 0111.25104
Birch, B. J.
12
1961
The addition of norm forms. Zbl 0105.02804
Birch, B. J.; Davenport, Harold; Lewis, D. J.
10
1962
Hecke actions on classes of ternary quadratic forms. Zbl 0748.11023
Birch, B. J.
9
1991
Elliptic curves over \(\mathbb{Q}\): A progress report. Zbl 0214.19801
Birch, B. J.
9
1971
Elliptic curves and modular functions. Zbl 0225.14016
Birch, B. J.
9
1970
Diophantine analysis and modular functions. Zbl 0246.10017
Birch, B. J.
9
1969
A criterion for the \(p\)-adic solubility of diophantine equations. Zbl 0269.10010
Birch, B. J.; McCann, K.
8
1967
Indefinite quadratic forms in many variables. Zbl 0084.27201
Birch, B. J.; Davenport, Harold
8
1958
Computation of Heegner points. Zbl 0559.14010
Birch, Bryan J.; Stephens, Nelson M.
7
1984
Some calculations of modular relations. Zbl 0261.10019
Birch, B. J.
7
1973
The inhomogeneous minimum of quadratic forms of signature zero. Zbl 0080.03405
Birch, B. J.
7
1958
Small zeros of diagonal forms of odd degree in many variables. Zbl 0198.37201
Birch, B. J.
7
1970
Computers in number theory. Proceedings of the science research council Atlas symposium No. 2 held at Oxford, from 18–23 August, 1969. Zbl 0214.00106
6
1971
Conjectures concerning elliptic curves. Zbl 0238.14011
Birch, B. J.
6
1965
Waring’s problem for \(p\)-adic number fields. Zbl 0131.28901
Birch, B. J.
6
1964
Multiplicative functions with non-decreasing normal order. Zbl 0159.05703
Birch, B. J.
6
1967
Heegner points: the beginnings. Zbl 1073.11001
Birch, Bryan
6
2004
\(p\)-adic forms. Zbl 0096.02503
Birch, B. J.; Lewis, D. J.
5
1960
Systems of three quadratic forms. Zbl 0152.01503
Birch, B. J.; Lewis, D. J.
4
1965
\(K_2\) of global fields. Zbl 0218.12010
Birch, B. J.
3
1971
On games with almost complete information. Zbl 0064.38303
Birch, B. J.
3
1955
A transference theorem of the geometry of numbers. Zbl 0071.27301
Birch, B. J.
2
1956
Diagonal equations over \(\mathfrak p\)-adic fields. Zbl 0146.27601
Birch, B. J.
2
1964
The collected papers of Hans Arnold Heilbronn. Zbl 0652.01038
Heilbronn, H. A.
2
1988
On p-adic forms. Zbl 0122.25405
Birch, B. J.; Lewis, D. J.
2
1962
Note on Weyl’s inequality. Zbl 0105.03801
Birch, B. J.; Davenport, Harold
2
1962
Correspondence. Zbl 1073.11002
Birch, Bryan; Gross, Benedict
2
2004
Heegner’s construction of points on the curve \(y^ 2=x^ 2-1728e^ 3\). Zbl 0535.14012
Birch, B. J.; Stephens, N. M.
2
1983
Heegner’s proof. Zbl 1357.11109
Birch, Bryan
1
2011
Sampling inspection tables for comparison of two groups using the negative binomial model. Zbl 0125.37402
Bennett, B. M.; Birch, B.
1
1964
The collected works of Harold Davenport. Vols. I, II, III and IV. Zbl 0383.01022
1
1977
Heegner’s proof. Zbl 1357.11109
Birch, Bryan
1
2011
Heegner points: the beginnings. Zbl 1073.11001
Birch, Bryan
6
2004
Correspondence. Zbl 1073.11002
Birch, Bryan; Gross, Benedict
2
2004
Noncongruence subgroups, covers and drawings. Zbl 0930.11024
Birch, Bryan
20
1994
Hecke actions on classes of ternary quadratic forms. Zbl 0748.11023
Birch, B. J.
9
1991
The collected papers of Hans Arnold Heilbronn. Zbl 0652.01038
Heilbronn, H. A.
2
1988
Incomplete Kloosterman sums and a divisor problem. Appendix: On some exponential sums by Bryan J. Birch and Enrico Bombieri. Zbl 0572.10029
Friedlander, John B.; Iwaniec, Henryk
59
1985
Computation of Heegner points. Zbl 0559.14010
Birch, Bryan J.; Stephens, Nelson M.
7
1984
Heegner’s construction of points on the curve \(y^ 2=x^ 2-1728e^ 3\). Zbl 0535.14012
Birch, B. J.; Stephens, N. M.
2
1983
The collected works of Harold Davenport. Vols. I, II, III and IV. Zbl 0383.01022
1
1977
On the orbit-sizes of permutation groups containing elements separating finite subsets. Zbl 0334.20003
Birch, B. J.; Burns, R. G.; Macdonald, Sheila Oates; Neumann, Peter M.
13
1976
Modular functions of one variable. IV. Proceedings of the international summer school, University of Antwerp, RUCA, July 17 – August 3, 1972. Zbl 0315.14014
58
1975
Elliptic curves and modular functions. Zbl 1214.11081
Swinnerton-Dyer, H. P. F.; Birch, B. J.
24
1975
A look back at Ramanujan’s notebooks. Zbl 0305.10002
Birch, B. J.
22
1975
Heegner points of elliptic curves. Zbl 0317.14015
Birch, B. J.
12
1975
The Hasse problem for rational surfaces. Zbl 0326.14007
Birch, B. J.; Swinnterton-Dyer, H. P. F.
16
1974
On a problem of Chowla. Zbl 0267.10065
Baker, A.; Birch, B. J.; Wirsing, E. A.
34
1973
Some calculations of modular relations. Zbl 0261.10019
Birch, B. J.
7
1973
Finiteness theorems for binary forms with given discriminant. Zbl 0248.12002
Birch, B. J.; Merriman, J. R.
31
1972
Elliptic curves over \(\mathbb{Q}\): A progress report. Zbl 0214.19801
Birch, B. J.
9
1971
Computers in number theory. Proceedings of the science research council Atlas symposium No. 2 held at Oxford, from 18–23 August, 1969. Zbl 0214.00106
6
1971
\(K_2\) of global fields. Zbl 0218.12010
Birch, B. J.
3
1971
Elliptic curves and modular functions. Zbl 0225.14016
Birch, B. J.
9
1970
Small zeros of diagonal forms of odd degree in many variables. Zbl 0198.37201
Birch, B. J.
7
1970
Weber’s class invariants. Zbl 0226.12005
Birch, B. J.
30
1969
Diophantine analysis and modular functions. Zbl 0246.10017
Birch, B. J.
9
1969
How the number of points of an elliptic curve over a fixed prime field varies. Zbl 0183.25503
Birch, B. J.
71
1968
Global class field theory. Zbl 1179.11041
Tate, J. T.
67
1967
Cyclotomic fields and Kummer extensions. Zbl 1492.11155
Birch, B. J.
15
1967
Complex multiplication. Zbl 1492.11104
Serre, J.-P.
12
1967
A criterion for the \(p\)-adic solubility of diophantine equations. Zbl 0269.10010
Birch, B. J.; McCann, K.
8
1967
Multiplicative functions with non-decreasing normal order. Zbl 0159.05703
Birch, B. J.
6
1967
The parity of the rank of the Mordell-Weil group. Zbl 0146.42401
Birch, B. J.; Stephens, N. M.
42
1966
Notes on elliptic curves. II. Zbl 0147.02506
Birch, B. J.; Swinnerton-Dyer, H. P. F.
116
1965
On the difference \(x^ 3 -y^ 2\). Zbl 0144.03901
Birch, B. J.; Chowla, Sarvadaman; Hall, M. jun.; Schinzel, Andrzej
12
1965
Conjectures concerning elliptic curves. Zbl 0238.14011
Birch, B. J.
6
1965
Systems of three quadratic forms. Zbl 0152.01503
Birch, B. J.; Lewis, D. J.
4
1965
Waring’s problem for \(p\)-adic number fields. Zbl 0131.28901
Birch, B. J.
6
1964
Diagonal equations over \(\mathfrak p\)-adic fields. Zbl 0146.27601
Birch, B. J.
2
1964
Sampling inspection tables for comparison of two groups using the negative binomial model. Zbl 0125.37402
Bennett, B. M.; Birch, B.
1
1964
Notes on elliptic curves. I. Zbl 0118.27601
Birch, B. J.; Swinnerton-Dyer, H. P. F.
65
1963
Forms in many variables. Zbl 0103.03102
Birch, B. J.
117
1962
Simultaneous quadratic forms. Zbl 0111.02001
Birch, B. J.; Lewis, D. J.; Murphy, T. G.
13
1962
The addition of norm forms. Zbl 0105.02804
Birch, B. J.; Davenport, Harold; Lewis, D. J.
10
1962
On p-adic forms. Zbl 0122.25405
Birch, B. J.; Lewis, D. J.
2
1962
Note on Weyl’s inequality. Zbl 0105.03801
Birch, B. J.; Davenport, Harold
2
1962
Waring’s problem in algebraic number fields. Zbl 0111.25104
Birch, B. J.
12
1961
\(p\)-adic forms. Zbl 0096.02503
Birch, B. J.; Lewis, D. J.
5
1960
Note on a problem of Chowla. Zbl 0091.04301
Birch, B. J.; Swinnerton-Dyer, H. P. F.
28
1959
On 3 \(N\) points in a plane. Zbl 0089.38502
Birch, B. J.
21
1959
Note on a problem of Erdős. Zbl 0093.05003
Birch, B. J.
18
1959
Quadratic equations in several variables. Zbl 0081.04401
Birch, B. J.; Davenport, Harold
12
1958
On a theorem of Davenport and Heilbronn. Zbl 0082.26002
Birch, B. J.; Davenport, Harold
12
1958
Indefinite quadratic forms in many variables. Zbl 0084.27201
Birch, B. J.; Davenport, Harold
8
1958
The inhomogeneous minimum of quadratic forms of signature zero. Zbl 0080.03405
Birch, B. J.
7
1958
Homogeneous forms of odd degree in a large number of variables. Zbl 0081.04501
Birch, B. J.
33
1957
On the inhomogeneous minimum of the product of n linear forms. Zbl 0074.03702
Birch, B. J.; Swinnerton-Dyer, H. P. F.
14
1956
A transference theorem of the geometry of numbers. Zbl 0071.27301
Birch, B. J.
2
1956
On games with almost complete information. Zbl 0064.38303
Birch, B. J.
3
1955
all top 5

Cited by 972 Authors

16 Murty, Maruti Ram
14 Shparlinski, Igor E.
11 Schmidt, Wolfgang M.
10 Browning, Timothy Daniel
10 Heath-Brown, Roger
9 Chen, Yonggao
9 Miller, Steven J.
9 Raka, Madhu
9 Schindler, Damaris
8 Bhargava, Manjul
8 González-Jiménez, Enrique
7 Cremona, John E.
7 Fisher, Tom A.
7 Hans-Gill, Rajinder J.
7 Wooley, Trevor D.
6 Cook, Brian
6 Fang, Jinhui
6 Magyar, Akos
6 Mazur, Barry
6 Ono, Ken
6 Rubin, Karl Cooper
6 Voight, John Michael
5 Bambah, R. P.
5 Brandes, Julia
5 Dietmann, Rainer
5 Dokchitser, Tim
5 Glazunov, Mykola Mykhaĭlovych
5 Jahnel, Jörg
5 Jeon, Daeyeol
5 Kathuria, Leetika
5 Parsell, Scott T.
5 Qin, Hourong
5 Silverberg, Alice
5 Skorobogatov, Alexei Nikolaïevitch
5 Yamagishi, Shuntaro
4 Bharadwaj, Abhishek T.
4 Byeon, Dongho
4 Coates, John Henry
4 Colliot-Thélène, Jean-Louis
4 Creutz, Brendan
4 Dokchitser, Vladimir
4 Dumir, Vishwa Chander
4 Elliott, Peter D. T. A.
4 Evertse, Jan-Hendrik
4 Flynn, Eugene Victor
4 Goldfeld, Dorian Morris
4 Gross, Benedict Hyman
4 Gun, Sanoli
4 Győry, Kálmán
4 Jeong, Keunyoung
4 Katz, Nicholas Michael
4 Leep, David B.
4 Lozano-Robledo, Álvaro
4 Morain, François
4 Pathak, Siddhi S.
4 Peyre, Emmanuel
4 Prabhu, Neha
4 Roudneff, Jean-Pierre
4 Saradha, N.
4 Sarnak, Peter Clive
4 Sawin, William F.
4 Schlickewei, Hans Peter
4 Sehmi, Ranjeet
4 Shankar, Arul
4 Sijsling, Jeroen
4 Siksek, Samir
4 Sofos, Efthymios
4 Sujatha, Ramdorai
4 Tanimoto, Sho
4 Vila, Núria
4 Vishe, Pankaj
3 Aggarwal, Satish Kumar
3 Akhtari, Shabnam
3 Barrios, Alexander J.
3 Bayer Isant, Pilar
3 Brüdern, Jörg
3 Bruinier, Jan Hendrik
3 Bulkhali, Nasser Abdo Saeed
3 Cameron, Peter Jephson
3 Chatterjee, Tapas
3 Cook, Roger J.
3 de la Bretèche, Régis
3 Derenthal, Ulrich
3 Dujella, Andrej
3 Duke, William Drexel
3 Elsenhans, Andreas-Stephan
3 Frey, Gerhard
3 Gelbart, Stephen S.
3 Granville, Andrew James
3 Guo, Xuejun
3 Harvey, M. P.
3 Hughes, Kevin
3 Kanemitsu, Shigeru
3 Kaplan, Nathan
3 Kim, Chang Heon
3 Kowalski, Emmanuel
3 Kraus, Alain
3 Lehmann, Brian
3 Loughran, Daniel
3 Michel, Philippe Gabriel
...and 872 more Authors
all top 5

Cited in 174 Serials

95 Journal of Number Theory
31 Mathematics of Computation
29 Compositio Mathematica
29 Inventiones Mathematicae
29 Transactions of the American Mathematical Society
25 International Journal of Number Theory
22 Duke Mathematical Journal
22 Journal de Théorie des Nombres de Bordeaux
20 Mathematische Annalen
18 Bulletin of the American Mathematical Society. New Series
17 Acta Arithmetica
16 Journal of Algebra
16 Monatshefte für Mathematik
15 Manuscripta Mathematica
14 Mathematische Zeitschrift
13 Advances in Mathematics
13 Annales de l’Institut Fourier
13 The Ramanujan Journal
12 Proceedings of the American Mathematical Society
12 Research in Number Theory
11 Rocky Mountain Journal of Mathematics
11 Mathematika
10 Israel Journal of Mathematics
10 Archiv der Mathematik
10 Journal für die Reine und Angewandte Mathematik
9 Mathematical Notes
9 Proceedings of the Japan Academy. Series A
8 Mathematical Proceedings of the Cambridge Philosophical Society
8 Journal of the London Mathematical Society. Second Series
8 Proceedings of the London Mathematical Society. Third Series
8 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
7 Journal of Soviet Mathematics
6 European Journal of Combinatorics
6 Finite Fields and their Applications
6 Annals of Mathematics. Second Series
6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
5 Bulletin of the London Mathematical Society
5 Glasgow Mathematical Journal
5 Journal of Pure and Applied Algebra
5 Indagationes Mathematicae. New Series
5 Experimental Mathematics
5 Kyushu Journal of Mathematics
4 Acta Mathematica
4 Functiones et Approximatio. Commentarii Mathematici
4 Mathematische Nachrichten
4 Journal of Symbolic Computation
4 Journal of the American Mathematical Society
4 Journal of Mathematical Sciences (New York)
4 Science China. Mathematics
4 Research in the Mathematical Sciences
3 Acta Mathematica Academiae Scientiarum Hungaricae
3 Bulletin of the Australian Mathematical Society
3 Communications in Algebra
3 Indian Journal of Pure & Applied Mathematics
3 Journal of Mathematical Analysis and Applications
3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
3 Journal of Combinatorial Theory. Series A
3 Michigan Mathematical Journal
3 Acta Mathematica Hungarica
3 Forum Mathematicum
3 Expositiones Mathematicae
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Selecta Mathematica. New Series
3 Journal of the European Mathematical Society (JEMS)
3 Acta Mathematica Sinica. English Series
3 Journal of the Institute of Mathematics of Jussieu
3 Oberwolfach Reports
3 Bulletin de la Société Mathématique de France. Supplément. Mémoires
3 Algebra & Number Theory
3 Forum of Mathematics, Sigma
2 Journal of Computational Physics
2 Journal of Statistical Physics
2 Lithuanian Mathematical Journal
2 Applied Mathematics and Computation
2 Canadian Mathematical Bulletin
2 Computing
2 The Journal of the Indian Mathematical Society. New Series
2 Memoirs of the American Mathematical Society
2 Nagoya Mathematical Journal
2 Pacific Journal of Mathematics
2 Annals of Pure and Applied Logic
2 Geometric and Functional Analysis. GAFA
2 L’Enseignement Mathématique. 2e Série
2 Cybernetics and Systems Analysis
2 Izvestiya: Mathematics
2 Documenta Mathematica
2 LMS Journal of Computation and Mathematics
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Bulletin of the American Mathematical Society
2 Albanian Journal of Mathematics
2 Involve
2 Discrete Analysis
2 Transactions of the American Mathematical Society. Series B
2 Annales Henri Lebesgue
1 Archive for History of Exact Sciences
1 Discrete Mathematics
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Journal d’Analyse Mathématique
1 Periodica Mathematica Hungarica
...and 74 more Serials
all top 5

Cited in 42 Fields

759 Number theory (11-XX)
302 Algebraic geometry (14-XX)
30 Field theory and polynomials (12-XX)
30 Group theory and generalizations (20-XX)
29 Combinatorics (05-XX)
29 Convex and discrete geometry (52-XX)
24 Special functions (33-XX)
14 History and biography (01-XX)
12 Probability theory and stochastic processes (60-XX)
11 Dynamical systems and ergodic theory (37-XX)
10 Functions of a complex variable (30-XX)
10 Computer science (68-XX)
9 Harmonic analysis on Euclidean spaces (42-XX)
8 Mathematical logic and foundations (03-XX)
8 Commutative algebra (13-XX)
8 \(K\)-theory (19-XX)
7 Topological groups, Lie groups (22-XX)
7 Information and communication theory, circuits (94-XX)
6 General and overarching topics; collections (00-XX)
6 Algebraic topology (55-XX)
5 Associative rings and algebras (16-XX)
5 Geometry (51-XX)
5 Manifolds and cell complexes (57-XX)
5 Quantum theory (81-XX)
4 Measure and integration (28-XX)
4 Ordinary differential equations (34-XX)
4 Functional analysis (46-XX)
4 Numerical analysis (65-XX)
3 Statistics (62-XX)
3 Statistical mechanics, structure of matter (82-XX)
3 Operations research, mathematical programming (90-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 Linear and multilinear algebra; matrix theory (15-XX)
2 Category theory; homological algebra (18-XX)
2 Real functions (26-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Integral equations (45-XX)
2 General topology (54-XX)
1 Nonassociative rings and algebras (17-XX)
1 Partial differential equations (35-XX)
1 Difference and functional equations (39-XX)
1 Differential geometry (53-XX)

Citations by Year

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.