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Borcherds, Richard Ewen

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Author ID: borcherds.richard-e Recent zbMATH articles by "Borcherds, Richard Ewen"
Published as: Borcherds, Richard E.; Borcherds, R. E.; Borcherds, Richard
Homepage: https://math.berkeley.edu/~reb/
External Links: MacTutor · MGP · Wikidata · Google Scholar · IdRef
Awards: EMS Prize (1992) · Fields Medal (1998)
Documents Indexed: 31 Publications since 1984
1 Further Contribution
Biographic References: 9 Publications
Co-Authors: 9 Co-Authors with 5 Joint Publications
343 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

32 Publications have been cited 2,033 times in 1,135 Documents Cited by Year
Vertex algebras, Kac-Moody algebras, and the monster. Zbl 0613.17012
Borcherds, Richard E.
502
1986
Sphere packings, lattices and groups. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. 3rd ed. Zbl 0915.52003
Conway, J. H.; Sloane, N. J. A.
406
1999
Automorphic forms with singularities on Grassmannians. Zbl 0919.11036
Borcherds, Richard E.
240
1998
Monstrous moonshine and monstrous Lie superalgebras. Zbl 0799.17014
Borcherds, Richard E.
214
1992
Generalized Kac-Moody algebras. Zbl 0644.17010
Borcherds, Richard
127
1988
Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products. Zbl 0932.11028
Borcherds, Richard E.
116
1995
The Gross-Kohnen-Zagier theorem in higher dimensions. Zbl 0967.11022
Borcherds, Richard E.
84
1999
Automorphism groups of Lorentzian lattices. Zbl 0628.20003
Borcherds, Richard
34
1987
Reflection groups of Lorentzian lattices. Zbl 0970.11015
Borcherds, Richard E.
33
2000
The monster Lie algebra. Zbl 0734.17010
Borcherds, Richard E.
28
1990
Coxeter groups, Lorentzian lattices, and \(K3\) surfaces. Zbl 0935.20027
Borcherds, Richard E.
26
1998
The moduli space of Enriques surfaces and the fake monster Lie superalgebra. Zbl 0886.14015
Borcherds, Richard E.
26
1996
Quantum vertex algebras. Zbl 1018.17018
Borcherds, Richard E.
24
2001
Families of K3 surfaces. Zbl 0946.14021
Borcherds, Richard E.; Katzarkov, Ludmil; Pantev, Tony; Shepherd-Barron, N. I.
22
1998
Modular moonshine. II. Zbl 1032.17049
Borcherds, Richard E.; Ryba, Alex J. E.
22
1996
Vertex algebras. Zbl 0956.17019
Borcherds, Richard E.
19
1998
Central extensions of generalized Kac-Moody algebras. Zbl 0776.17021
Borcherds, Richard E.
17
1991
Modular moonshine. III. Zbl 1047.17014
Borcherds, Richard E.
17
1998
The Leech lattice. Zbl 0558.10028
Borcherds, R. E.
16
1985
Lattices like the Leech lattice. Zbl 0701.11021
Borcherds, Richard E.
11
1990
A characterization of generalized Kac-Moody algebras. Zbl 0828.17031
Borcherds, Richard E.
11
1995
Automorphic forms on \(O_{s+2,2}(\mathbb{R})^ +\) and generalized Kac-Moody algebras. Zbl 0862.11034
Borcherds, Richard E.
7
1995
A monster Lie algebra? Zbl 0555.17004
Borcherds, R. E.; Conway, J. H.; Queen, L.; Sloane, N. J. A.
6
1984
A Siegel cusp form of degree 12 and weight 12. Zbl 0885.11034
Borcherds, Richard E.; Freitag, E.; Weissauer, R.
5
1998
What is moonshine. Zbl 1003.11017
Borcherds, Richard E.
4
1998
Introduction to the monster Lie algebra. Zbl 0839.11018
Borcherds, Richard E.
4
1992
Classification of positive definite lattices. Zbl 1017.11016
Borcherds, Richard E.
3
2000
Sporadic groups and string theory. Zbl 0828.17030
Borcherds, Richard E.
3
1994
Automorphic forms and Lie algebras. Zbl 0923.17024
Borcherds, Richard E.
2
1997
The fake monster formal group. Zbl 1018.17019
Borcherds, Richard E.
2
1999
Problems in moonshine. Zbl 1077.11503
Borcherds, Richard E.
1
2001
Renormalization and quantum field theory. Zbl 1243.22021
Borcherds, Richard E.
1
2011
Renormalization and quantum field theory. Zbl 1243.22021
Borcherds, Richard E.
1
2011
Quantum vertex algebras. Zbl 1018.17018
Borcherds, Richard E.
24
2001
Problems in moonshine. Zbl 1077.11503
Borcherds, Richard E.
1
2001
Reflection groups of Lorentzian lattices. Zbl 0970.11015
Borcherds, Richard E.
33
2000
Classification of positive definite lattices. Zbl 1017.11016
Borcherds, Richard E.
3
2000
Sphere packings, lattices and groups. With additional contributions by E. Bannai, R. E. Borcherds, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. 3rd ed. Zbl 0915.52003
Conway, J. H.; Sloane, N. J. A.
406
1999
The Gross-Kohnen-Zagier theorem in higher dimensions. Zbl 0967.11022
Borcherds, Richard E.
84
1999
The fake monster formal group. Zbl 1018.17019
Borcherds, Richard E.
2
1999
Automorphic forms with singularities on Grassmannians. Zbl 0919.11036
Borcherds, Richard E.
240
1998
Coxeter groups, Lorentzian lattices, and \(K3\) surfaces. Zbl 0935.20027
Borcherds, Richard E.
26
1998
Families of K3 surfaces. Zbl 0946.14021
Borcherds, Richard E.; Katzarkov, Ludmil; Pantev, Tony; Shepherd-Barron, N. I.
22
1998
Vertex algebras. Zbl 0956.17019
Borcherds, Richard E.
19
1998
Modular moonshine. III. Zbl 1047.17014
Borcherds, Richard E.
17
1998
A Siegel cusp form of degree 12 and weight 12. Zbl 0885.11034
Borcherds, Richard E.; Freitag, E.; Weissauer, R.
5
1998
What is moonshine. Zbl 1003.11017
Borcherds, Richard E.
4
1998
Automorphic forms and Lie algebras. Zbl 0923.17024
Borcherds, Richard E.
2
1997
The moduli space of Enriques surfaces and the fake monster Lie superalgebra. Zbl 0886.14015
Borcherds, Richard E.
26
1996
Modular moonshine. II. Zbl 1032.17049
Borcherds, Richard E.; Ryba, Alex J. E.
22
1996
Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products. Zbl 0932.11028
Borcherds, Richard E.
116
1995
A characterization of generalized Kac-Moody algebras. Zbl 0828.17031
Borcherds, Richard E.
11
1995
Automorphic forms on \(O_{s+2,2}(\mathbb{R})^ +\) and generalized Kac-Moody algebras. Zbl 0862.11034
Borcherds, Richard E.
7
1995
Sporadic groups and string theory. Zbl 0828.17030
Borcherds, Richard E.
3
1994
Monstrous moonshine and monstrous Lie superalgebras. Zbl 0799.17014
Borcherds, Richard E.
214
1992
Introduction to the monster Lie algebra. Zbl 0839.11018
Borcherds, Richard E.
4
1992
Central extensions of generalized Kac-Moody algebras. Zbl 0776.17021
Borcherds, Richard E.
17
1991
The monster Lie algebra. Zbl 0734.17010
Borcherds, Richard E.
28
1990
Lattices like the Leech lattice. Zbl 0701.11021
Borcherds, Richard E.
11
1990
Generalized Kac-Moody algebras. Zbl 0644.17010
Borcherds, Richard
127
1988
Automorphism groups of Lorentzian lattices. Zbl 0628.20003
Borcherds, Richard
34
1987
Vertex algebras, Kac-Moody algebras, and the monster. Zbl 0613.17012
Borcherds, Richard E.
502
1986
The Leech lattice. Zbl 0558.10028
Borcherds, R. E.
16
1985
A monster Lie algebra? Zbl 0555.17004
Borcherds, R. E.; Conway, J. H.; Queen, L.; Sloane, N. J. A.
6
1984
all top 5

Cited by 828 Authors

53 Dong, Chongying
40 Li, Haisheng
28 Bruinier, Jan Hendrik
22 Linshaw, Andrew Ross
19 Huang, Yi-Zhi
19 Mason, Geoffrey
17 Bringmann, Kathrin
17 Kac, Victor G.
17 Kim, Chang Heon
16 Duncan, John F. R.
15 Gritsenko, Valeriĭ Alekseevich
15 Lam, Ching Hung
15 Schwagenscheidt, Markus
14 Kang, Seok-Jin
14 Lepowsky, James
14 Miyamoto, Masahiko
14 Ono, Ken
13 Borcherds, Richard Ewen
13 Shimakura, Hiroki
12 Williams, Brandon
10 Arakawa, Tomoyuki
10 Bakalov, Bojko
10 Creutzig, Thomas
10 Jiang, Cuipo
10 Naito, Satoshi
10 Scheithauer, Nils R.
10 Tanabe, Kenichiro
10 Yamskulna, Gaywalee
9 Folsom, Amanda L.
9 Li, Yingkun
9 Lim, Subong
9 Milas, Antun
9 Mu, Qiang
9 Raum, Martin
9 Ren, Li
9 Shimada, Ichiro
9 Xu, Xiaoping
9 Yang, Tonghai
8 Choi, Dohoon
8 Kondō, Shigeyuki
8 Koo, Jakyung
8 Lin, Xingjun
8 Wang, Haowu
7 Ai, Chunrui
7 Allcock, Daniel Jonathan
7 Calinescu, Corina
7 Cheng, Miranda C. N.
7 Frenkel, Edward V.
7 Heim, Bernhard Ernst
7 Jurisich, Elizabeth
7 Kane, Ben
7 Klemm, Albrecht
7 Kolesnikov, Pavel Sergeevich
7 Krieg, Aloys
7 Moore, Gregory Winthrop
7 Yu, Nina
7 Zemel, Shaul
6 De Sole, Alberto
6 Ehlen, Stephan Jakob
6 Freitag, Eberhard
6 Griess, Robert L. jun.
6 Imamoḡlu, Özlem
6 Lee, Kyu-Hwan
6 Lian, Bong H.
6 Liberati, Jose I.
6 Nikulin, Vyacheslav Valentinovich
6 Perše, Ozren
6 Sthanumoorthy, Neelacanta
6 Tan, Shao Bin
6 Tuite, Michael P.
6 van Ekeren, Jethro
6 Wu, Zhixiang
6 Ye, Dongxi
5 Abe, Toshiyuki
5 Alfes-Neumann, Claudia
5 Barron, Katrina
5 Choie, YoungJu
5 Duke, William Drexel
5 Griffin, Michael J.
5 Han, Jianzhi
5 Harrison, Sarah M.
5 Harvey, Jeffrey A.
5 Höhn, Gerald
5 Jiao, Xiangyu
5 Kim, Henry H.
5 Kožić, Slaven
5 Kříž, Igor
5 Lilly, P. L.
5 Nikolov, Nikolay M.
5 Paquette, Natalie M.
5 Pioline, Boris
5 Ray, Urmie
5 Roitman, Michael
5 Salvati Manni, Riccardo
5 Shpectorov, Sergey Viktorovich
5 Sun, Jiancai
5 Volpato, Roberto
4 Adamović, Dražen
4 Anguelova, Iana I.
4 Beneish, Lea
...and 728 more Authors
all top 5

Cited in 158 Serials

163 Journal of Algebra
75 Communications in Mathematical Physics
59 Advances in Mathematics
48 Communications in Algebra
46 Journal of Pure and Applied Algebra
44 Journal of High Energy Physics
37 Transactions of the American Mathematical Society
33 Journal of Number Theory
30 Journal of Mathematical Physics
28 Duke Mathematical Journal
26 Communications in Contemporary Mathematics
25 Mathematische Zeitschrift
20 The Ramanujan Journal
19 Nuclear Physics. B
17 Proceedings of the American Mathematical Society
15 Compositio Mathematica
15 International Journal of Mathematics
14 Inventiones Mathematicae
14 International Journal of Number Theory
12 Mathematische Annalen
11 Letters in Mathematical Physics
11 Research in Number Theory
9 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
9 Journal für die Reine und Angewandte Mathematik
9 Bulletin of the American Mathematical Society. New Series
9 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
9 Science China. Mathematics
8 Nagoya Mathematical Journal
8 Proceedings of the Japan Academy. Series A
8 Forum Mathematicum
8 Journal of Algebraic Geometry
8 Research in the Mathematical Sciences
7 Israel Journal of Mathematics
7 Selecta Mathematica. New Series
7 Transformation Groups
7 Journal of Physics A: Mathematical and Theoretical
6 Publications of the Research Institute for Mathematical Sciences, Kyoto University
6 Experimental Mathematics
6 Algebra Colloquium
6 Journal of Algebra and its Applications
5 Journal of Mathematical Sciences (New York)
5 Algebras and Representation Theory
4 International Journal of Modern Physics A
4 Journal of Mathematical Analysis and Applications
4 Mathematical Proceedings of the Cambridge Philosophical Society
4 Mathematics of Computation
4 Journal of Geometry and Physics
4 Michigan Mathematical Journal
4 Transactions of the Moscow Mathematical Society
4 Proceedings of the National Academy of Sciences of the United States of America
4 Journal de Théorie des Nombres de Bordeaux
4 Annals of Mathematics. Second Series
4 Frontiers of Mathematics in China
4 Forum of Mathematics, Sigma
3 Canadian Journal of Mathematics
3 Journal of Combinatorial Theory. Series A
3 Journal of the Mathematical Society of Japan
3 Memoirs of the American Mathematical Society
3 European Journal of Combinatorics
3 Advances in Applied Mathematics
3 Nuclear Physics. B. Proceedings Supplements
3 Representation Theory
3 Journal of Group Theory
3 Journal of the European Mathematical Society (JEMS)
3 Acta Mathematica Sinica. English Series
3 Annales Henri Poincaré
3 Oberwolfach Reports
3 Japanese Journal of Mathematics. 3rd Series
3 Open Mathematics
2 Bulletin of the Australian Mathematical Society
2 General Relativity and Gravitation
2 Rocky Mountain Journal of Mathematics
2 Theoretical and Mathematical Physics
2 Reviews in Mathematical Physics
2 Acta Arithmetica
2 Acta Mathematica
2 Algebra and Logic
2 Annales de l’Institut Fourier
2 Geometriae Dedicata
2 Mathematika
2 Tohoku Mathematical Journal. Second Series
2 Acta Applicandae Mathematicae
2 Journal of Symbolic Computation
2 Journal of the American Mathematical Society
2 Sugaku Expositions
2 Geometry & Topology
2 LMS Journal of Computation and Mathematics
2 Journal of the Australian Mathematical Society
2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
2 International Journal of Geometric Methods in Modern Physics
2 Forum of Mathematics, Pi
2 Annales Mathématiques du Québec
2 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
2 Electronic Research Archive
1 Modern Physics Letters A
1 Computer Physics Communications
1 International Journal of Theoretical Physics
1 Linear and Multilinear Algebra
1 Mathematical Notes
1 Reports on Mathematical Physics
...and 58 more Serials
all top 5

Cited in 45 Fields

635 Nonassociative rings and algebras (17-XX)
410 Number theory (11-XX)
232 Quantum theory (81-XX)
165 Algebraic geometry (14-XX)
121 Group theory and generalizations (20-XX)
64 Associative rings and algebras (16-XX)
44 Relativity and gravitational theory (83-XX)
30 Category theory; homological algebra (18-XX)
30 Several complex variables and analytic spaces (32-XX)
27 Topological groups, Lie groups (22-XX)
26 Differential geometry (53-XX)
22 Global analysis, analysis on manifolds (58-XX)
20 Combinatorics (05-XX)
20 Geometry (51-XX)
17 Special functions (33-XX)
15 Manifolds and cell complexes (57-XX)
11 Convex and discrete geometry (52-XX)
11 Information and communication theory, circuits (94-XX)
9 Commutative algebra (13-XX)
9 Dynamical systems and ergodic theory (37-XX)
8 Functions of a complex variable (30-XX)
7 Statistical mechanics, structure of matter (82-XX)
6 \(K\)-theory (19-XX)
5 General and overarching topics; collections (00-XX)
5 Functional analysis (46-XX)
5 Algebraic topology (55-XX)
4 History and biography (01-XX)
4 Partial differential equations (35-XX)
3 Field theory and polynomials (12-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Operator theory (47-XX)
3 Mechanics of particles and systems (70-XX)
2 Approximations and expansions (41-XX)
2 Computer science (68-XX)
1 General algebraic systems (08-XX)
1 Real functions (26-XX)
1 Ordinary differential equations (34-XX)
1 Difference and functional equations (39-XX)
1 Sequences, series, summability (40-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Abstract harmonic analysis (43-XX)
1 Probability theory and stochastic processes (60-XX)
1 Statistics (62-XX)
1 Fluid mechanics (76-XX)
1 Astronomy and astrophysics (85-XX)

Citations by Year

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