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Birch, Bryan John

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Author ID: birch.bryan-j Recent zbMATH articles by "Birch, Bryan John"
Published as: Birch, B.; Birch, B. J.; Birch, Bryan; Birch, Bryan J.
Homepage: https://www.maths.ox.ac.uk/people/bryan.birch
External Links: MGP · Math-Net.Ru · Wikidata · GND
Documents Indexed: 66 Publications since 1955, including 3 Books

Publications by Year

Citations contained in zbMATH Open

53 Publications have been cited 752 times in 654 Documents Cited by Year
Forms in many variables. Zbl 0103.03102
Birch, B. J.
80
1962
Notes on elliptic curves. II. Zbl 0147.02506
Birch, B. J.; Swinnerton-Dyer, H. P. F.
78
1965
How the number of points of an elliptic curve over a fixed prime field varies. Zbl 0183.25503
Birch, B. J.
50
1968
Modular functions of one variable. IV. Proceedings of the international summer school, University of Antwerp, RUCA, July 17 - August 3, 1972. Zbl 0315.14014
Birch, B. J. (ed.); Kuyk, W. (ed.)
49
1975
Notes on elliptic curves. I. Zbl 0118.27601
Birch, B. J.; Swinnerton-Dyer, H. P. F.
49
1963
The parity of the rank of the Mordell-Weil group. Zbl 0146.42401
Birch, B. J.; Stephens, N. M.
30
1966
Homogeneous forms of odd degree in a large number of variables. Zbl 0081.04501
Birch, B. J.
28
1957
Weber’s class invariants. Zbl 0226.12005
Birch, B. J.
27
1969
On a problem of Chowla. Zbl 0267.10065
Baker, A.; Birch, B. J.; Wirsing, E. A.
24
1973
Note on a problem of Chowla. Zbl 0091.04301
Birch, B. J.; Swinnerton-Dyer, H. P. F.
21
1959
A look back at Ramanujan’s notebooks. Zbl 0305.10002
Birch, B. J.
20
1975
Finiteness theorems for binary forms with given discriminant. Zbl 0248.12002
Birch, B. J.; Merriman, J. R.
20
1972
On 3 \(N\) points in a plane. Zbl 0089.38502
Birch, B. J.
18
1959
Elliptic curves and modular functions. Zbl 1214.11081
Swinnerton-Dyer, H. P. F.; Birch, B. J.
17
1975
Noncongruence subgroups, covers and drawings. Zbl 0930.11024
Birch, Bryan
15
1994
On the inhomogeneous minimum of the product of n linear forms. Zbl 0074.03702
Birch, B. J.; Swinnerton-Dyer, H. P. F.
13
1956
Simultaneous quadratic forms. Zbl 0111.02001
Birch, B. J.; Lewis, D. J.; Murphy, T. G.
12
1962
Note on a problem of Erdős. Zbl 0093.05003
Birch, B. J.
12
1959
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.
11
1976
Heegner points of elliptic curves. Zbl 0317.14015
Birch, B. J.
10
1975
The Hasse problem for rational surfaces. Zbl 0326.14007
Birch, B. J.; Swinnterton-Dyer, H. P. F.
10
1974
The addition of norm forms. Zbl 0105.02804
Birch, B. J.; Davenport, Harold; Lewis, D. J.
10
1962
On a theorem of Davenport and Heilbronn. Zbl 0082.26002
Birch, B. J.; Davenport, Harold
10
1958
Quadratic equations in several variables. Zbl 0081.04401
Birch, B. J.; Davenport, Harold
10
1958
On the difference \(x^ 3 -y^ 2\). Zbl 0144.03901
Birch, B. J.; Chowla, Sarvadaman; Hall, M. jun.; Schinzel, Andrzej
9
1965
Waring’s problem in algebraic number fields. Zbl 0111.25104
Birch, B. J.
9
1961
Computation of Heegner points. Zbl 0559.14010
Birch, Bryan J.; Stephens, Nelson M.
8
1984
Elliptic curves and modular functions. Zbl 0225.14016
Birch, B. J.
7
1970
Small zeros of diagonal forms of odd degree in many variables. Zbl 0198.37201
Birch, B. J.
7
1970
Indefinite quadratic forms in many variables. Zbl 0084.27201
Birch, B. J.; Davenport, Harold
7
1958
The inhomogeneous minimum of quadratic forms of signature zero. Zbl 0080.03405
Birch, B. J.
7
1958
A criterion for the \(p\)-adic solubility of diophantine equations. Zbl 0269.10010
Birch, B. J.; McCann, K.
6
1967
Multiplicative functions with non-decreasing normal order. Zbl 0159.05703
Birch, B. J.
6
1967
Heegner points: the beginnings. Zbl 1073.11001
Birch, Bryan
5
2004
Some calculations of modular relations. Zbl 0261.10019
Birch, B. J.
5
1973
Elliptic curves over \(\mathbb{Q}\): A progress report. Zbl 0214.19801
Birch, B. J.
5
1971
Conjectures concerning elliptic curves. Zbl 0238.14011
Birch, B. J.
5
1965
Waring’s problem for \(p\)-adic number fields. Zbl 0131.28901
Birch, B. J.
5
1964
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
Atkin, A. O. L. (ed.); Birch, B. J. (ed.)
4
1971
Diophantine analysis and modular functions. Zbl 0246.10017
Birch, B. J.
4
1969
Systems of three quadratic forms. Zbl 0152.01503
Birch, B. J.; Lewis, D. J.
4
1965
\(p\)-adic forms. Zbl 0096.02503
Birch, B. J.; Lewis, D. J.
4
1960
Hecke actions on classes of ternary quadratic forms. Zbl 0748.11023
Birch, B. J.
3
1991
On games with almost complete information. Zbl 0064.38303
Birch, B. J.
3
1955
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
\(K_ 2\) of global fields. Zbl 0218.12010
Birch, B. J.
2
1971
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
A transference theorem of the geometry of numbers. Zbl 0071.27301
Birch, B. J.
2
1956
Heegner’s proof. Zbl 1357.11109
Birch, Bryan
1
2011
The collected works of Harold Davenport. Vols. I, II, III and IV. Zbl 0383.01022
Birch, B. J. (ed.); Halberstam, H. (ed.); Rogers, C. A. (ed.)
1
1977
Sampling inspection tables for comparison of two groups using the negative binomial model. Zbl 0125.37402
Bennett, B. M.; Birch, B.
1
1964
Heegner’s proof. Zbl 1357.11109
Birch, Bryan
1
2011
Heegner points: the beginnings. Zbl 1073.11001
Birch, Bryan
5
2004
Correspondence. Zbl 1073.11002
Birch, Bryan; Gross, Benedict
2
2004
Noncongruence subgroups, covers and drawings. Zbl 0930.11024
Birch, Bryan
15
1994
Hecke actions on classes of ternary quadratic forms. Zbl 0748.11023
Birch, B. J.
3
1991
Computation of Heegner points. Zbl 0559.14010
Birch, Bryan J.; Stephens, Nelson M.
8
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
Birch, B. J. (ed.); Halberstam, H. (ed.); Rogers, C. A. (ed.)
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.
11
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
Birch, B. J. (ed.); Kuyk, W. (ed.)
49
1975
A look back at Ramanujan’s notebooks. Zbl 0305.10002
Birch, B. J.
20
1975
Elliptic curves and modular functions. Zbl 1214.11081
Swinnerton-Dyer, H. P. F.; Birch, B. J.
17
1975
Heegner points of elliptic curves. Zbl 0317.14015
Birch, B. J.
10
1975
The Hasse problem for rational surfaces. Zbl 0326.14007
Birch, B. J.; Swinnterton-Dyer, H. P. F.
10
1974
On a problem of Chowla. Zbl 0267.10065
Baker, A.; Birch, B. J.; Wirsing, E. A.
24
1973
Some calculations of modular relations. Zbl 0261.10019
Birch, B. J.
5
1973
Finiteness theorems for binary forms with given discriminant. Zbl 0248.12002
Birch, B. J.; Merriman, J. R.
20
1972
Elliptic curves over \(\mathbb{Q}\): A progress report. Zbl 0214.19801
Birch, B. J.
5
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
Atkin, A. O. L. (ed.); Birch, B. J. (ed.)
4
1971
\(K_ 2\) of global fields. Zbl 0218.12010
Birch, B. J.
2
1971
Elliptic curves and modular functions. Zbl 0225.14016
Birch, B. J.
7
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.
27
1969
Diophantine analysis and modular functions. Zbl 0246.10017
Birch, B. J.
4
1969
How the number of points of an elliptic curve over a fixed prime field varies. Zbl 0183.25503
Birch, B. J.
50
1968
A criterion for the \(p\)-adic solubility of diophantine equations. Zbl 0269.10010
Birch, B. J.; McCann, K.
6
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.
30
1966
Notes on elliptic curves. II. Zbl 0147.02506
Birch, B. J.; Swinnerton-Dyer, H. P. F.
78
1965
On the difference \(x^ 3 -y^ 2\). Zbl 0144.03901
Birch, B. J.; Chowla, Sarvadaman; Hall, M. jun.; Schinzel, Andrzej
9
1965
Conjectures concerning elliptic curves. Zbl 0238.14011
Birch, B. J.
5
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.
5
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.
49
1963
Forms in many variables. Zbl 0103.03102
Birch, B. J.
80
1962
Simultaneous quadratic forms. Zbl 0111.02001
Birch, B. J.; Lewis, D. J.; Murphy, T. G.
12
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.
9
1961
\(p\)-adic forms. Zbl 0096.02503
Birch, B. J.; Lewis, D. J.
4
1960
Note on a problem of Chowla. Zbl 0091.04301
Birch, B. J.; Swinnerton-Dyer, H. P. F.
21
1959
On 3 \(N\) points in a plane. Zbl 0089.38502
Birch, B. J.
18
1959
Note on a problem of Erdős. Zbl 0093.05003
Birch, B. J.
12
1959
On a theorem of Davenport and Heilbronn. Zbl 0082.26002
Birch, B. J.; Davenport, Harold
10
1958
Quadratic equations in several variables. Zbl 0081.04401
Birch, B. J.; Davenport, Harold
10
1958
Indefinite quadratic forms in many variables. Zbl 0084.27201
Birch, B. J.; Davenport, Harold
7
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.
28
1957
On the inhomogeneous minimum of the product of n linear forms. Zbl 0074.03702
Birch, B. J.; Swinnerton-Dyer, H. P. F.
13
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 703 Authors

13 Murty, Maruti Ram
11 Schmidt, Wolfgang M.
11 Shparlinski, Igor E.
10 Heath-Brown, Roger
8 Browning, Timothy Daniel
8 Raka, Madhu
7 Hans-Gill, Rajinder J.
6 Fang, Jinhui
6 Mazur, Barry
6 Rubin, Karl Cooper
6 Wooley, Trevor D.
5 Bambah, R. P.
5 Chen, Yonggao
5 Cremona, John E.
5 Miller, Steven J.
5 Ono, Ken
5 Parsell, Scott T.
5 Schindler, Damaris
5 Silverberg, Alice
5 Skorobogatov, Alexei Nikolaïevitch
4 Byeon, Dongho
4 Dietmann, Rainer
4 Dokchitser, Tim
4 Dokchitser, Vladimir
4 Dumir, Vishwa Chander
4 Elliott, Peter D. T. A.
4 Fisher, Tom A.
4 Flynn, Eugene Victor
4 Glazunov, Mykola Mykhaĭlovych
4 González-Jiménez, Enrique
4 Kathuria, Leetika
4 Katz, Nicholas Michael
4 Morain, François
4 Prabhu, Neha
4 Roudneff, Jean-Pierre
4 Saradha, N.
4 Sarnak, Peter Clive
4 Sehmi, Ranjeet
4 Shankar, Arul
4 Siksek, Samir
4 Vila, Núria
3 Aggarwal, Satish Kumar
3 Bayer Isant, Pilar
3 Bharadwaj, Abhishek T.
3 Bhargava, Manjul
3 Brandes, Julia
3 Brüdern, Jörg
3 Cameron, Peter Jephson
3 Coates, John H.
3 Cook, Brian
3 Creutz, Brendan
3 Dujella, Andrej
3 Duke, William Drexel
3 Frey, Gerhard
3 Gelbart, Stephen S.
3 Goldfeld, Dorian Morris
3 Granville, Andrew James
3 Gross, Benedict Hyman
3 Győry, Kálmán
3 Harvey, M. P.
3 Jeon, Daeyeol
3 Jeong, Keunyoung
3 Lozano-Robledo, Álvaro
3 Munshi, Ritabrata
3 Peyre, Emmanuel
3 Plans, Bernat
3 Podsypanin, Evgeniĭ Vladimirovich
3 Praeger, Cheryl Elisabeth
3 Qin, Hourong
3 Sawin, William F.
3 Schlickewei, Hans Peter
3 Schulze-Pillot, Rainer
3 Sijsling, Jeroen
3 Spencer, Craig V.
3 Ramdorai, Sujatha
3 Top, Jaap
3 Várilly-Alvarado, Anthony
3 Xiao, Stanley Yao
3 Yamagishi, Shuntaro
3 Zhang, Liangcheng
2 Adiga, Chandrashekar
2 Andrews, George Eyre
2 Arias-de-Reyna, Sara
2 Baier, Stephan
2 Baker, Roger C.
2 Baxter, Rodney J.
2 Bertolini, Massimo
2 Bettin, Sandro
2 Blagojević, Pavle V. M.
2 Blanco-Chacón, Iván
2 Bosser, Vincent
2 Bremner, Andrew
2 Bruinier, Jan Hendrik
2 Bulkhali, Nasser Abdo Saeed
2 Canci, Jung Kyu
2 Chang, Mei-Chu
2 Chatterjee, Tapas
2 Chen, Imin
2 Cochrane, Todd
2 Colliot-Thélène, Jean-Louis
...and 603 more Authors
all top 5

Cited in 141 Serials

79 Journal of Number Theory
26 Inventiones Mathematicae
25 Mathematics of Computation
24 Compositio Mathematica
21 Duke Mathematical Journal
21 Journal de Théorie des Nombres de Bordeaux
20 Transactions of the American Mathematical Society
17 Bulletin of the American Mathematical Society. New Series
17 International Journal of Number Theory
16 Mathematische Annalen
14 Journal of Algebra
14 Manuscripta Mathematica
13 Advances in Mathematics
13 Monatshefte für Mathematik
12 Mathematische Zeitschrift
10 Mathematika
9 Israel Journal of Mathematics
9 Mathematical Notes
9 Rocky Mountain Journal of Mathematics
9 Annales de l’Institut Fourier
9 Archiv der Mathematik
9 Proceedings of the American Mathematical Society
9 Proceedings of the Japan Academy. Series A
9 The Ramanujan Journal
7 Acta Arithmetica
7 Journal of Soviet Mathematics
6 Mathematical Proceedings of the Cambridge Philosophical Society
6 Journal für die Reine und Angewandte Mathematik
6 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
5 Glasgow Mathematical Journal
5 European Journal of Combinatorics
5 Finite Fields and their Applications
5 Annals of Mathematics. Second Series
5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
4 Acta Mathematica
4 Journal of the American Mathematical Society
4 Indagationes Mathematicae. New Series
3 Acta Mathematica Academiae Scientiarum Hungaricae
3 Bulletin of the Australian Mathematical Society
3 Indian Journal of Pure & Applied Mathematics
3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
3 Functiones et Approximatio. Commentarii Mathematici
3 Journal of Combinatorial Theory. Series A
3 Acta Mathematica Hungarica
3 Journal of Symbolic Computation
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Acta Mathematica Sinica. English Series
3 Bulletin de la Société Mathématique de France. Supplément. Mémoires
3 Science China. Mathematics
3 Research in Number Theory
2 Communications in Algebra
2 Journal of Mathematical Analysis and Applications
2 Journal of Statistical Physics
2 Lithuanian Mathematical Journal
2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
2 Applied Mathematics and Computation
2 Bulletin of the London Mathematical Society
2 Computing
2 The Journal of the Indian Mathematical Society. New Series
2 Journal of the London Mathematical Society. Second Series
2 Michigan Mathematical Journal
2 Nagoya Mathematical Journal
2 Forum Mathematicum
2 Geometric and Functional Analysis. GAFA
2 Expositiones Mathematicae
2 Experimental Mathematics
2 Journal of Mathematical Sciences (New York)
2 Kyushu Journal of Mathematics
2 Selecta Mathematica. New Series
2 Documenta Mathematica
2 LMS Journal of Computation and Mathematics
2 Journal of the European Mathematical Society (JEMS)
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Bulletin of the American Mathematical Society
2 Forum of Mathematics, Sigma
2 Research in the Mathematical Sciences
1 Archive for History of Exact Sciences
1 Discrete Mathematics
1 Journal d’Analyse Mathématique
1 Periodica Mathematica Hungarica
1 Annali di Matematica Pura ed Applicata. Serie Quarta
1 The Annals of Statistics
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
1 BIT
1 Canadian Journal of Mathematics
1 Canadian Mathematical Bulletin
1 Commentarii Mathematici Helvetici
1 Czechoslovak Mathematical Journal
1 Publications Mathématiques
1 International Journal of Game Theory
1 Journal of Computational and Applied Mathematics
1 Journal of Differential Equations
1 Journal of Pure and Applied Algebra
1 The Journal of Symbolic Logic
1 Kyungpook Mathematical Journal
1 Memoirs of the American Mathematical Society
1 Pacific Journal of Mathematics
1 Proceedings of the London Mathematical Society. Third Series
1 Programming and Computer Software
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
...and 41 more Serials
all top 5

Cited in 38 Fields

557 Number theory (11-XX)
225 Algebraic geometry (14-XX)
27 Field theory and polynomials (12-XX)
25 Convex and discrete geometry (52-XX)
23 Combinatorics (05-XX)
19 Group theory and generalizations (20-XX)
19 Special functions (33-XX)
10 History and biography (01-XX)
10 Probability theory and stochastic processes (60-XX)
8 Functions of a complex variable (30-XX)
6 Commutative algebra (13-XX)
6 \(K\)-theory (19-XX)
5 Mathematical logic and foundations (03-XX)
5 Dynamical systems and ergodic theory (37-XX)
5 Information and communication theory, circuits (94-XX)
4 Topological groups, Lie groups (22-XX)
4 Ordinary differential equations (34-XX)
4 Functional analysis (46-XX)
4 Geometry (51-XX)
4 Algebraic topology (55-XX)
4 Manifolds and cell complexes (57-XX)
3 Associative rings and algebras (16-XX)
3 Measure and integration (28-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
3 Computer science (68-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 Real functions (26-XX)
2 General topology (54-XX)
2 Statistics (62-XX)
2 Quantum theory (81-XX)
1 Nonassociative rings and algebras (17-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Partial differential equations (35-XX)
1 Differential geometry (53-XX)
1 Numerical analysis (65-XX)

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