Edit Profile (opens in new tab) Borcherds, Richard Ewen Co-Author Distance Author ID: borcherds.richard-e Published as: Borcherds, Richard E.; Borcherds, Richard; Borcherds, R. E. more...less Homepage: https://math.berkeley.edu/~reb/ External Links: MacTutor · MGP · Wikidata · Google Scholar · IdRef Awards: EMS Prize (1992) · Fields Medal (1998) Documents Indexed: 36 Publications since 1984, including 5 Additional arXiv Preprints 2 Further Contributions Biographic References: 9 Publications Co-Authors: 9 Co-Authors with 6 Joint Publications 387 Co-Co-Authors all top 5 Co-Authors 31 single-authored 2 Conway, John Horton 2 Queen, Larissa 2 Ryba, Alexander J. E. 2 Sloane, Neil James Alexander 1 Bannai, Eiichi 1 Bhargava, Manjul 1 Curtis, Robert T. 1 Freitag, Eberhard 1 Gilman, Jane P. 1 Katzarkov, Ludmil 1 Kauffman, Louis Hirsch 1 Leech, John 1 Norton, Simon Phillips 1 Odlyzko, Andrew M. 1 Pantev, Tony G. 1 Parker, Richard A. 1 Schleicher, Dierk 1 Shepherd-Barron, Nicholas Ian 1 Siegel, Aaron Nathan 1 Venkov, Boris B. 1 Weissauer, Rainer all top 5 Serials 6 Duke Mathematical Journal 5 Journal of Algebra 3 Inventiones Mathematicae 2 Advances in Mathematics 1 Journal für die Reine und Angewandte Mathematik 1 Topology 1 IMRN. International Mathematics Research Notices 1 Proceedings of the National Academy of Sciences of the United States of America 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 Notices of the American Mathematical Society 1 Journal of Algebraic Geometry 1 Documenta Mathematica 1 Grundlehren der Mathematischen Wissenschaften 1 Algebra & Number Theory all top 5 Fields 23 Number theory (11-XX) 21 Nonassociative rings and algebras (17-XX) 18 Group theory and generalizations (20-XX) 4 Algebraic geometry (14-XX) 3 Topological groups, Lie groups (22-XX) 3 Geometry (51-XX) 3 Quantum theory (81-XX) 2 Combinatorics (05-XX) 2 Convex and discrete geometry (52-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 32 Publications have been cited 1,980 times in 1,375 Documents Cited by ▼ Year ▼ 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. 613 1999 Vertex algebras, Kac-Moody algebras, and the monster. Zbl 0613.17012 Borcherds, Richard E. 580 1986 Automorphic forms with singularities on Grassmannians. Zbl 0919.11036 Borcherds, Richard E. 308 1998 Monstrous moonshine and monstrous Lie superalgebras. Zbl 0799.17014 Borcherds, Richard E. 258 1992 Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products. Zbl 0932.11028 Borcherds, Richard E. 159 1995 Generalized Kac-Moody algebras. Zbl 0644.17010 Borcherds, Richard 149 1988 The Gross-Kohnen-Zagier theorem in higher dimensions. Zbl 0967.11022 Borcherds, Richard E. 114 1999 The monster Lie algebra. Zbl 0734.17010 Borcherds, Richard E. 40 1990 Automorphism groups of Lorentzian lattices. Zbl 0628.20003 Borcherds, Richard 39 1987 Reflection groups of Lorentzian lattices. Zbl 0970.11015 Borcherds, Richard E. 37 2000 Families of K3 surfaces. Zbl 0946.14021 Borcherds, Richard E.; Katzarkov, Ludmil; Pantev, Tony; Shepherd-Barron, N. I. 31 1998 The moduli space of Enriques surfaces and the fake monster Lie superalgebra. Zbl 0886.14015 Borcherds, Richard E. 31 1996 Coxeter groups, Lorentzian lattices, and \(K3\) surfaces. Zbl 0935.20027 Borcherds, Richard E. 29 1998 Quantum vertex algebras. Zbl 1018.17018 Borcherds, Richard E. 27 2001 Modular moonshine. II. Zbl 1032.17049 Borcherds, Richard E.; Ryba, Alex J. E. 25 1996 Vertex algebras. Zbl 0956.17019 Borcherds, Richard E. 23 1998 The Leech lattice. Zbl 0558.10028 Borcherds, R. E. 21 1985 Central extensions of generalized Kac-Moody algebras. Zbl 0776.17021 Borcherds, Richard E. 20 1991 Modular moonshine. III. Zbl 1047.17014 Borcherds, Richard E. 19 1998 A characterization of generalized Kac-Moody algebras. Zbl 0828.17031 Borcherds, Richard E. 12 1995 Lattices like the Leech lattice. Zbl 0701.11021 Borcherds, Richard E. 12 1990 Automorphic forms on \(O_{s+2,2}(\mathbb{R})^ +\) and generalized Kac-Moody algebras. Zbl 0862.11034 Borcherds, Richard E. 8 1995 A Siegel cusp form of degree 12 and weight 12. Zbl 0885.11034 Borcherds, Richard E.; Freitag, E.; Weissauer, R. 7 1998 A monster Lie algebra? Zbl 0555.17004 Borcherds, R. E.; Conway, J. H.; Queen, L.; Sloane, N. J. A. 7 1984 What is moonshine. Zbl 1003.11017 Borcherds, Richard E. 5 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. 4 2000 Renormalization and quantum field theory. Zbl 1243.22021 Borcherds, Richard E. 3 2011 Sporadic groups and string theory. Zbl 0828.17030 Borcherds, Richard E. 3 1994 The fake monster formal group. Zbl 1018.17019 Borcherds, Richard E. 2 1999 Automorphic forms and Lie algebras. Zbl 0923.17024 Borcherds, Richard E. 2 1997 Problems in moonshine. Zbl 1077.11503 Borcherds, Richard E. 1 2001 Renormalization and quantum field theory. Zbl 1243.22021 Borcherds, Richard E. 3 2011 Quantum vertex algebras. Zbl 1018.17018 Borcherds, Richard E. 27 2001 Problems in moonshine. Zbl 1077.11503 Borcherds, Richard E. 1 2001 Reflection groups of Lorentzian lattices. Zbl 0970.11015 Borcherds, Richard E. 37 2000 Classification of positive definite lattices. Zbl 1017.11016 Borcherds, Richard E. 4 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. 613 1999 The Gross-Kohnen-Zagier theorem in higher dimensions. Zbl 0967.11022 Borcherds, Richard E. 114 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. 308 1998 Families of K3 surfaces. Zbl 0946.14021 Borcherds, Richard E.; Katzarkov, Ludmil; Pantev, Tony; Shepherd-Barron, N. I. 31 1998 Coxeter groups, Lorentzian lattices, and \(K3\) surfaces. Zbl 0935.20027 Borcherds, Richard E. 29 1998 Vertex algebras. Zbl 0956.17019 Borcherds, Richard E. 23 1998 Modular moonshine. III. Zbl 1047.17014 Borcherds, Richard E. 19 1998 A Siegel cusp form of degree 12 and weight 12. Zbl 0885.11034 Borcherds, Richard E.; Freitag, E.; Weissauer, R. 7 1998 What is moonshine. Zbl 1003.11017 Borcherds, Richard E. 5 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. 31 1996 Modular moonshine. II. Zbl 1032.17049 Borcherds, Richard E.; Ryba, Alex J. E. 25 1996 Automorphic forms on \(O_{s+2,2}(\mathbb R)\) and infinite products. Zbl 0932.11028 Borcherds, Richard E. 159 1995 A characterization of generalized Kac-Moody algebras. Zbl 0828.17031 Borcherds, Richard E. 12 1995 Automorphic forms on \(O_{s+2,2}(\mathbb{R})^ +\) and generalized Kac-Moody algebras. Zbl 0862.11034 Borcherds, Richard E. 8 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. 258 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. 20 1991 The monster Lie algebra. Zbl 0734.17010 Borcherds, Richard E. 40 1990 Lattices like the Leech lattice. Zbl 0701.11021 Borcherds, Richard E. 12 1990 Generalized Kac-Moody algebras. Zbl 0644.17010 Borcherds, Richard 149 1988 Automorphism groups of Lorentzian lattices. Zbl 0628.20003 Borcherds, Richard 39 1987 Vertex algebras, Kac-Moody algebras, and the monster. Zbl 0613.17012 Borcherds, Richard E. 580 1986 The Leech lattice. Zbl 0558.10028 Borcherds, R. E. 21 1985 A monster Lie algebra? Zbl 0555.17004 Borcherds, R. E.; Conway, J. H.; Queen, L.; Sloane, N. J. A. 7 1984 all cited Publications top 5 cited Publications all top 5 Cited by 1,020 Authors 58 Dong, Chongying 53 Li, Haisheng 30 Bruinier, Jan Hendrik 24 Linshaw, Andrew Ross 23 Mason, Geoffrey 22 Huang, Yi-Zhi 20 Lam, Ching Hung 19 Bringmann, Kathrin 19 Kim, Chang Heon 19 Williams, Brandon 18 Duncan, John F. R. 18 Kac, Victor 18 Schwagenscheidt, Markus 17 Wang, Haowu 16 Ono, Ken 15 Gritsenko, Valeriĭ Alekseevich 15 Kang, Seok-Jin 15 Lepowsky, James 15 Miyamoto, Masahiko 15 Shimakura, Hiroki 13 Borcherds, Richard Ewen 13 Jiang, Cuipo 13 Li, Yingkun 12 Creutzig, Thomas 12 Ren, Li 12 Scheithauer, Nils R. 12 Shimada, Ichiro 11 Milas, Antun 11 Naito, Satoshi 11 Raum, Martin 10 Arakawa, Tomoyuki 10 Bakalov, Bojko 10 Kondō, Shigeyuki 10 Mu, Qiang 10 Tanabe, Kenichiro 10 Tuite, Michael P. 10 Yamskulna, Gaywalee 10 Yang, Tonghai 10 Zemel, Shaul 9 Folsom, Amanda L. 9 Lim, Subong 9 Lin, Xingjun 9 Volpato, Roberto 9 Wang, Qing 9 Xu, Xiaoping 8 Cheng, Miranda C. N. 8 Choi, Dohoon 8 Heim, Bernhard Ernst 8 Jurisich, Elizabeth 8 Kane, Ben 8 Klemm, Albrecht 8 Kolesnikov, Pavel Sergeevich 8 Koo, Jakyung 8 Kožić, Slaven 8 Krieg, Aloys 8 Moore, Gregory Winthrop 8 Tan, Shaobin 8 Yu, Nina 7 Ai, Chunrui 7 Alfes-Neumann, Claudia 7 Allcock, Daniel Jonathan 7 Calinescu, Corina 7 Frenkel, Edward V. 7 Griess, Robert L. jun. 7 Harvey, Jeffrey A. 7 Ma, Shouhei 7 Paquette, Natalie M. 7 Perše, Ozren 7 van Ekeren, Jethro 7 Xu, Feng 7 Ye, Dongxi 6 Adamović, Dražen 6 Boyallian, Carina 6 De Sole, Alberto 6 Ehlen, Stephan Jakob 6 Freitag, Eberhard 6 Funke, Jens 6 Griffin, Michael J. 6 Harrison, Sarah M. 6 Hohenegger, Stefan 6 Höhn, Gerald 6 Imamoḡlu, Özlem 6 Jiao, Xiangyu 6 Keller, Christoph A. 6 Lee, Kyu-Hwan 6 Lian, Bong H. 6 Liberati, Jose I. 6 Lin, Zongzhu 6 Maeda, Yota 6 Nikolov, Nikolay M. 6 Nikulin, Vyacheslav Valentinovich 6 Palmkvist, Jakob 6 Sthanumoorthy, Neelacanta 6 Wu, Zhixiang 6 Zuevsky, Alexander 5 Abe, Toshiyuki 5 Anguelova, Iana I. 5 Barron, Katrina 5 Beneish, Lea 5 Carnahan, Scott Huai-Lei ...and 920 more Authors all top 5 Cited in 179 Serials 177 Journal of Algebra 87 Communications in Mathematical Physics 67 Advances in Mathematics 63 Journal of High Energy Physics 50 Communications in Algebra 48 Journal of Pure and Applied Algebra 40 Transactions of the American Mathematical Society 39 Journal of Number Theory 36 Journal of Mathematical Physics 30 Nuclear Physics. B 29 Duke Mathematical Journal 28 Communications in Contemporary Mathematics 25 Mathematische Zeitschrift 25 The Ramanujan Journal 19 Proceedings of the American Mathematical Society 18 International Journal of Number Theory 17 Compositio Mathematica 17 Journal of Physics A: Mathematical and Theoretical 17 Research in Number Theory 16 Inventiones Mathematicae 16 Mathematische Annalen 16 International Journal of Mathematics 15 Letters in Mathematical Physics 11 Forum Mathematicum 11 Bulletin of the American Mathematical Society. New Series 11 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 10 Journal of Algebra and its Applications 9 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 9 Journal für die Reine und Angewandte Mathematik 9 Nagoya Mathematical Journal 9 Science China. Mathematics 9 Research in the Mathematical Sciences 8 Proceedings of the Japan Academy. Series A 8 Experimental Mathematics 8 Journal of Algebraic Geometry 8 Transformation Groups 7 Israel Journal of Mathematics 7 Publications of the Research Institute for Mathematical Sciences, Kyoto University 7 Selecta Mathematica. New Series 7 Algebras and Representation Theory 6 Mathematics of Computation 6 Algebra Colloquium 6 Annales Henri Poincaré 6 Algebra & Number Theory 6 Forum of Mathematics, Sigma 5 Journal of Mathematical Analysis and Applications 5 Journal of Geometry and Physics 5 Bulletin of the London Mathematical Society 5 Journal of Mathematical Sciences (New York) 5 Annals of Mathematics. Second Series 5 Oberwolfach Reports 4 International Journal of Modern Physics A 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Canadian Journal of Mathematics 4 Journal of Combinatorial Theory. Series A 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 Nuclear Physics. B. Proceedings Supplements 4 Journal de Théorie des Nombres de Bordeaux 4 Journal of the European Mathematical Society (JEMS) 4 Frontiers of Mathematics in China 4 Japanese Journal of Mathematics. 3rd Series 3 Linear and Multilinear Algebra 3 Reviews in Mathematical Physics 3 Acta Arithmetica 3 Geometriae Dedicata 3 Journal of the Mathematical Society of Japan 3 Mathematika 3 Memoirs of the American Mathematical Society 3 European Journal of Combinatorics 3 Advances in Applied Mathematics 3 Journal of Algebraic Combinatorics 3 Representation Theory 3 Geometry & Topology 3 Journal of Group Theory 3 Acta Mathematica Sinica. English Series 3 Forum of Mathematics, Pi 3 Open Mathematics 2 Bulletin of the Australian Mathematical Society 2 General Relativity and Gravitation 2 Physics Letters. B 2 Rocky Mountain Journal of Mathematics 2 Theoretical and Mathematical Physics 2 Chaos, Solitons and Fractals 2 Acta Mathematica 2 Algebra and Logic 2 Annales de l’Institut Fourier 2 Journal of the London Mathematical Society. Second Series 2 Manuscripta Mathematica 2 Pacific Journal of Mathematics 2 Tôhoku Mathematical Journal. Second Series 2 Chinese Annals of Mathematics. Series B 2 Acta Applicandae Mathematicae 2 Journal of Symbolic Computation 2 Journal of the American Mathematical Society 2 Sugaku Expositions 2 LMS Journal of Computation and Mathematics 2 Journal of the Australian Mathematical Society 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series ...and 79 more Serials all top 5 Cited in 49 Fields 749 Nonassociative rings and algebras (17-XX) 510 Number theory (11-XX) 312 Quantum theory (81-XX) 218 Algebraic geometry (14-XX) 139 Group theory and generalizations (20-XX) 79 Associative rings and algebras (16-XX) 57 Relativity and gravitational theory (83-XX) 41 Several complex variables and analytic spaces (32-XX) 37 Category theory; homological algebra (18-XX) 35 Topological groups, Lie groups (22-XX) 30 Differential geometry (53-XX) 28 Geometry (51-XX) 27 Combinatorics (05-XX) 25 Global analysis, analysis on manifolds (58-XX) 20 Manifolds and cell complexes (57-XX) 18 Special functions (33-XX) 17 Convex and discrete geometry (52-XX) 13 Information and communication theory, circuits (94-XX) 12 Commutative algebra (13-XX) 12 Functions of a complex variable (30-XX) 12 Dynamical systems and ergodic theory (37-XX) 11 Statistical mechanics, structure of matter (82-XX) 9 Functional analysis (46-XX) 8 \(K\)-theory (19-XX) 7 General and overarching topics; collections (00-XX) 7 Operator theory (47-XX) 7 Algebraic topology (55-XX) 6 Partial differential equations (35-XX) 5 Statistics (62-XX) 4 History and biography (01-XX) 4 Approximations and expansions (41-XX) 3 Field theory and polynomials (12-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Mechanics of particles and systems (70-XX) 2 Computer science (68-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-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 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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