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Author ID: birch.bryan-j Recent zbMATH articles by "Birch, Bryan John"
Published as: Birch, B. J.; Birch, Bryan; Birch, B.; Birch, Bryan J.
Further Spellings: Бёрч Брайан
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

57 Publications have been cited 925 times in 807 Documents Cited by Year
Forms in many variables. Zbl 0103.03102
Birch, B. J.
111
1962
Notes on elliptic curves. II. Zbl 0147.02506
Birch, B. J.; Swinnerton-Dyer, H. P. F.
104
1965
How the number of points of an elliptic curve over a fixed prime field varies. Zbl 0183.25503
Birch, B. J.
65
1968
Global class field theory. Zbl 1179.11041
Tate, J. T.
61
1967
Notes on elliptic curves. I. Zbl 0118.27601
Birch, B. J.; Swinnerton-Dyer, H. P. F.
61
1963
Modular functions of one variable. IV. Proceedings of the international summer school, University of Antwerp, RUCA, July 17 – August 3, 1972. Zbl 0315.14014
57
1975
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
55
1985
The parity of the rank of the Mordell-Weil group. Zbl 0146.42401
Birch, B. J.; Stephens, N. M.
39
1966
Homogeneous forms of odd degree in a large number of variables. Zbl 0081.04501
Birch, B. J.
32
1957
On a problem of Chowla. Zbl 0267.10065
Baker, A.; Birch, B. J.; Wirsing, E. A.
31
1973
Weber’s class invariants. Zbl 0226.12005
Birch, B. J.
30
1969
Finiteness theorems for binary forms with given discriminant. Zbl 0248.12002
Birch, B. J.; Merriman, J. R.
27
1972
Note on a problem of Chowla. Zbl 0091.04301
Birch, B. J.; Swinnerton-Dyer, H. P. F.
24
1959
On 3 \(N\) points in a plane. Zbl 0089.38502
Birch, B. J.
21
1959
A look back at Ramanujan’s notebooks. Zbl 0305.10002
Birch, B. J.
21
1975
Elliptic curves and modular functions. Zbl 1214.11081
Swinnerton-Dyer, H. P. F.; Birch, B. J.
19
1975
Noncongruence subgroups, covers and drawings. Zbl 0930.11024
Birch, Bryan
17
1994
Note on a problem of Erdős. Zbl 0093.05003
Birch, B. J.
16
1959
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
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
Simultaneous quadratic forms. Zbl 0111.02001
Birch, B. J.; Lewis, D. J.; Murphy, T. G.
12
1962
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.
12
1974
On the difference \(x^ 3 -y^ 2\). Zbl 0144.03901
Birch, B. J.; Chowla, Sarvadaman; Hall, M. jun.; Schinzel, Andrzej
11
1965
The addition of norm forms. Zbl 0105.02804
Birch, B. J.; Davenport, Harold; Lewis, D. J.
10
1962
Waring’s problem in algebraic number fields. Zbl 0111.25104
Birch, B. J.
9
1961
Elliptic curves and modular functions. Zbl 0225.14016
Birch, B. J.
9
1970
Cyclotomic fields and Kummer extensions. Zbl 1492.11155
Birch, B. J.
9
1967
Complex multiplication. Zbl 1492.11104
Serre, J.-P.
9
1967
Indefinite quadratic forms in many variables. Zbl 0084.27201
Birch, B. J.; Davenport, Harold
8
1958
A criterion for the \(p\)-adic solubility of diophantine equations. Zbl 0269.10010
Birch, B. J.; McCann, K.
8
1967
Computation of Heegner points. Zbl 0559.14010
Birch, Bryan J.; Stephens, Nelson M.
7
1984
The inhomogeneous minimum of quadratic forms of signature zero. Zbl 0080.03405
Birch, B. J.
7
1958
Elliptic curves over \(\mathbb{Q}\): A progress report. Zbl 0214.19801
Birch, B. J.
7
1971
Small zeros of diagonal forms of odd degree in many variables. Zbl 0198.37201
Birch, B. J.
7
1970
Multiplicative functions with non-decreasing normal order. Zbl 0159.05703
Birch, B. J.
6
1967
Hecke actions on classes of ternary quadratic forms. Zbl 0748.11023
Birch, B. J.
6
1991
\(p\)-adic forms. Zbl 0096.02503
Birch, B. J.; Lewis, D. J.
5
1960
Waring’s problem for \(p\)-adic number fields. Zbl 0131.28901
Birch, B. J.
5
1964
Diophantine analysis and modular functions. Zbl 0246.10017
Birch, B. J.
5
1969
Some calculations of modular relations. Zbl 0261.10019
Birch, B. J.
5
1973
Heegner points: the beginnings. Zbl 1073.11001
Birch, Bryan
5
2004
Correspondence. Zbl 1073.11002
Birch, Bryan; Gross, Benedict
5
2004
Systems of three quadratic forms. Zbl 0152.01503
Birch, B. J.; Lewis, D. J.
4
1965
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
4
1971
Conjectures concerning elliptic curves. Zbl 0238.14011
Birch, B. J.
4
1965
On games with almost complete information. Zbl 0064.38303
Birch, B. J.
3
1955
On p-adic forms. Zbl 0122.25405
Birch, B. J.; Lewis, D. J.
3
1962
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
A transference theorem of the geometry of numbers. Zbl 0071.27301
Birch, B. J.
2
1956
Note on Weyl’s inequality. Zbl 0105.03801
Birch, B. J.; Davenport, Harold
2
1962
\(K_ 2\) of global fields. Zbl 0218.12010
Birch, B. J.
2
1971
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
5
2004
Correspondence. Zbl 1073.11002
Birch, Bryan; Gross, Benedict
5
2004
Noncongruence subgroups, covers and drawings. Zbl 0930.11024
Birch, Bryan
17
1994
Hecke actions on classes of ternary quadratic forms. Zbl 0748.11023
Birch, B. J.
6
1991
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
55
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
57
1975
A look back at Ramanujan’s notebooks. Zbl 0305.10002
Birch, B. J.
21
1975
Elliptic curves and modular functions. Zbl 1214.11081
Swinnerton-Dyer, H. P. F.; Birch, B. J.
19
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.
12
1974
On a problem of Chowla. Zbl 0267.10065
Baker, A.; Birch, B. J.; Wirsing, E. A.
31
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.
27
1972
Elliptic curves over \(\mathbb{Q}\): A progress report. Zbl 0214.19801
Birch, B. J.
7
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
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.
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.
5
1969
How the number of points of an elliptic curve over a fixed prime field varies. Zbl 0183.25503
Birch, B. J.
65
1968
Global class field theory. Zbl 1179.11041
Tate, J. T.
61
1967
Cyclotomic fields and Kummer extensions. Zbl 1492.11155
Birch, B. J.
9
1967
Complex multiplication. Zbl 1492.11104
Serre, J.-P.
9
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.
39
1966
Notes on elliptic curves. II. Zbl 0147.02506
Birch, B. J.; Swinnerton-Dyer, H. P. F.
104
1965
On the difference \(x^ 3 -y^ 2\). Zbl 0144.03901
Birch, B. J.; Chowla, Sarvadaman; Hall, M. jun.; Schinzel, Andrzej
11
1965
Systems of three quadratic forms. Zbl 0152.01503
Birch, B. J.; Lewis, D. J.
4
1965
Conjectures concerning elliptic curves. Zbl 0238.14011
Birch, B. 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.
61
1963
Forms in many variables. Zbl 0103.03102
Birch, B. J.
111
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.
3
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.
5
1960
Note on a problem of Chowla. Zbl 0091.04301
Birch, B. J.; Swinnerton-Dyer, H. P. F.
24
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.
16
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.
32
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 875 Authors

15 Murty, Maruti Ram
12 Shparlinski, Igor E.
11 Schmidt, Wolfgang M.
10 Heath-Brown, Roger
9 Browning, Timothy Daniel
9 Chen, Yonggao
9 Raka, Madhu
7 González-Jiménez, Enrique
7 Hans-Gill, Rajinder J.
7 Miller, Steven J.
6 Bhargava, Manjul
6 Cook, Brian
6 Cremona, John E.
6 Fang, Jinhui
6 Fisher, Tom A.
6 Magyar, Akos
6 Mazur, Barry
6 Rubin, Karl Cooper
6 Schindler, Damaris
6 Wooley, Trevor D.
5 Bambah, R. P.
5 Brandes, Julia
5 Dietmann, Rainer
5 Glazunov, Mykola Mykhaĭlovych
5 Jeon, Daeyeol
5 Kathuria, Leetika
5 Ono, Ken
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 Creutz, Brendan
4 Dokchitser, Tim
4 Dumir, Vishwa Chander
4 Elliott, Peter D. T. A.
4 Flynn, Eugene Victor
4 Goldfeld, Dorian Morris
4 Gross, Benedict Hyman
4 Gun, Sanoli
4 Jeong, Keunyoung
4 Katz, Nicholas Michael
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 Ramdorai, Sujatha
4 Vila, Núria
4 Voight, John Michael
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 Coates, John Henry
3 Colliot-Thélène, Jean-Louis
3 de la Bretèche, Régis
3 Dokchitser, Vladimir
3 Dujella, Andrej
3 Duke, William Drexel
3 Elsenhans, Andreas-Stephan
3 Evertse, Jan-Hendrik
3 Frey, Gerhard
3 Gelbart, Stephen S.
3 Granville, Andrew James
3 Guo, Xuejun
3 Győry, Kálmán
3 Harvey, M. P.
3 Hughes, Kevin
3 Jahnel, Jörg
3 Kanemitsu, Shigeru
3 Kim, Chang Heon
3 Kowalski, Emmanuel
3 Kraus, Alain
3 Leep, David B.
3 Lehmann, Brian
3 Loughran, Daniel
3 Lozano-Robledo, Álvaro
3 Michel, Philippe Gabriel
3 Mirek, Mariusz
3 Monsky, Paul
3 Munshi, Ritabrata
3 Plans, Bernat
3 Podsypanin, Evgeniĭ Vladimirovich
...and 775 more Authors
all top 5

Cited in 167 Serials

92 Journal of Number Theory
28 Mathematics of Computation
28 Inventiones Mathematicae
27 Compositio Mathematica
24 Transactions of the American Mathematical Society
23 International Journal of Number Theory
22 Duke Mathematical Journal
22 Journal de Théorie des Nombres de Bordeaux
19 Mathematische Annalen
17 Bulletin of the American Mathematical Society. New Series
16 Journal of Algebra
16 Monatshefte für Mathematik
14 Manuscripta Mathematica
14 Mathematische Zeitschrift
13 Advances in Mathematics
12 Annales de l’Institut Fourier
12 Proceedings of the American Mathematical Society
12 The Ramanujan Journal
11 Acta Arithmetica
11 Mathematika
10 Israel Journal of Mathematics
10 Archiv der Mathematik
10 Research in Number Theory
9 Mathematical Notes
9 Rocky Mountain Journal of Mathematics
9 Journal für die Reine und Angewandte Mathematik
9 Proceedings of the Japan Academy. Series A
8 Mathematical Proceedings of the Cambridge Philosophical Society
8 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
7 Journal of Soviet Mathematics
6 European Journal of Combinatorics
6 Annals of Mathematics. Second Series
5 Glasgow Mathematical Journal
5 Finite Fields and their Applications
5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
4 Acta Mathematica
4 Bulletin of the London Mathematical Society
4 Functiones et Approximatio. Commentarii Mathematici
4 Journal of the London Mathematical Society. Second Series
4 Journal of Pure and Applied Algebra
4 Journal of the American Mathematical Society
4 Indagationes Mathematicae. New Series
4 Experimental Mathematics
4 Kyushu Journal of Mathematics
4 Science China. Mathematics
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 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 Proceedings of the London Mathematical Society. Third Series
3 Acta Mathematica Hungarica
3 Journal of Symbolic Computation
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 Oberwolfach Reports
3 Bulletin de la Société Mathématique de France. Supplément. Mémoires
3 Research in the Mathematical Sciences
2 Journal of Mathematical Analysis and Applications
2 Journal of Statistical Physics
2 Lithuanian Mathematical Journal
2 Applied Mathematics and Computation
2 Computing
2 The Journal of the Indian Mathematical Society. New Series
2 Michigan Mathematical Journal
2 Nagoya Mathematical Journal
2 Pacific Journal of Mathematics
2 Annals of Pure and Applied Logic
2 Geometric and Functional Analysis. GAFA
2 Cybernetics and Systems Analysis
2 Journal of Mathematical Sciences (New York)
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 Algebra & Number Theory
2 Albanian Journal of Mathematics
2 Forum of Mathematics, Sigma
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
1 The Mathematical Intelligencer
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
...and 67 more Serials
all top 5

Cited in 42 Fields

687 Number theory (11-XX)
273 Algebraic geometry (14-XX)
30 Field theory and polynomials (12-XX)
29 Group theory and generalizations (20-XX)
29 Convex and discrete geometry (52-XX)
27 Combinatorics (05-XX)
21 Special functions (33-XX)
12 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)
9 Harmonic analysis on Euclidean spaces (42-XX)
7 Mathematical logic and foundations (03-XX)
7 Commutative algebra (13-XX)
7 \(K\)-theory (19-XX)
7 Topological groups, Lie groups (22-XX)
7 Computer science (68-XX)
7 Information and communication theory, circuits (94-XX)
5 Associative rings and algebras (16-XX)
5 Geometry (51-XX)
5 Manifolds and cell complexes (57-XX)
4 General and overarching topics; collections (00-XX)
4 Measure and integration (28-XX)
4 Ordinary differential equations (34-XX)
4 Functional analysis (46-XX)
4 Algebraic topology (55-XX)
4 Quantum theory (81-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 Real functions (26-XX)
2 Integral equations (45-XX)
2 General topology (54-XX)
2 Numerical analysis (65-XX)
1 Nonassociative rings and algebras (17-XX)
1 Category theory; homological algebra (18-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Partial differential equations (35-XX)
1 Difference and functional equations (39-XX)
1 Differential geometry (53-XX)

Citations by Year

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