# zbMATH — the first resource for mathematics

## Schoof, René

Compute Distance To:
 Author ID: schoof.rene Published as: Schoof, R.; Schoof, R. J.; Schoof, René External Links: MGP · Wikidata
 Documents Indexed: 52 Publications since 1980, including 2 Books Reviewing Activity: 69 Reviews
all top 5

#### Co-Authors

 31 single-authored 3 Van der Geer, Gerard 3 Washington, Lawrence C. 2 Kraft, James Stuart 2 van der Vlugt, Marcel 1 Bayer-Fluckiger, Eva 1 Corrales-Rodrigáñez, Capi 1 de Smit, Bart 1 Dose, Valerio 1 Fernandez, Julio 1 González, Josep R. 1 Lario, Joan-Carles 1 Larsen, Michael Jeffrey 1 Lenstra, Hendrik W. jun. 1 Mercuri, Pietro 1 Mestre, Jean-François 1 Monsurrò, Marina 1 Moonen, Ben 1 Parimala, Raman 1 Rubin, Karl Cooper 1 Schappacher, Norbert 1 Talamanca, Valerio 1 Tzanakis, Nikos 1 Van de Craats, Jan 1 Zagier, Don Bernard
all top 5

#### Serials

 8 Mathematics of Computation 5 Journal of Number Theory 4 Compositio Mathematica 2 Journal of Combinatorial Theory. Series A 2 Experimental Mathematics 2 Journal de Théorie des Nombres de Bordeaux 1 The Mathematical Intelligencer 1 Acta Arithmetica 1 Gazette des Mathématiciens 1 Journal of Algebra 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Pacific Journal of Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Nieuw Archief voor Wiskunde. Vierde Serie 1 Selecta Mathematica. New Series 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Progress in Mathematics 1 Universitext
all top 5

#### Fields

 44 Number theory (11-XX) 23 Algebraic geometry (14-XX) 5 Information and communication theory, circuits (94-XX) 3 General and overarching topics; collections (00-XX) 3 Field theory and polynomials (12-XX) 3 Group theory and generalizations (20-XX) 2 Commutative algebra (13-XX) 2 Computer science (68-XX) 1 History and biography (01-XX) 1 Associative rings and algebras (16-XX) 1 Category theory; homological algebra (18-XX)

#### Citations contained in zbMATH

38 Publications have been cited 652 times in 582 Documents Cited by Year
Elliptic curves over finite fields and the computation of square roots mod p. Zbl 0579.14025
Schoof, René
1985
Nonsingular plane cubic curves over finite fields. Zbl 0632.14021
Schoof, René
1987
Counting points on elliptic curves over finite fields. Zbl 0852.11073
Schoof, René
1995
Primitive normal bases for finite fields. Zbl 0615.12023
Lenstra, H. W. jun.; Schoof, R. J.
1987
Quintic polynomials and real cyclotomic fields with large class numbers. Zbl 0649.12007
Schoof, René; Washington, Lawrence C.
1988
Computing Iwasawa modules of real quadratic number fields. Zbl 0840.11043
Kraft, James S.; Schoof, René
1995
Hecke operators and the weight distributions of certain codes. Zbl 0729.11065
Schoof, René; van der Vlugt, Marcel
1991
The support problem and its elliptic analogue. Zbl 0922.11086
Corrales-Rodrigáñez, Capi; Schoof, René
1997
Families of curves and weight distributions of codes. Zbl 0854.11072
Schoof, René
1995
Class numbers of real cyclotomic fields of prime conductor. Zbl 1052.11071
Schoof, René
2003
Infinite class field towers of quadratic fields. Zbl 0589.12011
Schoof, René
1986
Effectivity of Arakelov divisors and the theta divisor of a number field. Zbl 1030.11063
van der Geer, Gerard; Schoof, René
2000
Computing Arakelov class groups. Zbl 1188.11076
Schoof, René
2008
Minus class groups of the fields of the $$l$$-th roots of unity. Zbl 0902.11043
Schoof, René
1998
Algebraic curves over $${\mathbb{F}}_ 2$$ with many rational points. Zbl 0762.11026
Schoof, René
1992
Abelian varieties over $$\mathbb Q$$ with bad reduction in one prime only. Zbl 1173.11333
Schoof, René
2005
Abelian varieties over cyclotomic fields with good reduction everywhere. Zbl 1058.11038
Schoof, René
2003
Beppo Levi and the arithmetic of elliptic curves. Zbl 0849.01036
Schappacher, Norbert; Schoof, René
1996
Weight formulas for ternary Melas codes. Zbl 0768.94017
van der Geer, Gerard; Schoof, René; van der Vlugt, Marcel
1992
The exponents of the groups of points on the reductions of an elliptic curve. Zbl 0726.14023
Schoof, René
1991
Criteria for complete intersections. Zbl 0903.13003
De Smit, Bart; Rubin, Karl; Schoof, René
1997
The automorphism group of the non-split Cartan modular curve of level 11. Zbl 1330.14049
Dose, Valerio; Fernández, Julio; González, Josep; Schoof, René
2014
Semistable abelian varieties with good reduction outside 15. Zbl 1323.11040
Schoof, René
2012
Visibility of ideal classes. Zbl 1226.11123
Schoof, René; Washington, Lawrence C.
2010
Catalan’s conjecture. Zbl 1186.11018
Schoof, René
2008
Class groups of complex quadratic fields. Zbl 0516.12002
Schoof, R. J.
1983
Integral points of a modular curve of level 11. Zbl 1292.11057
Schoof, René; Tzanakis, Nikos
2012
Four primality testing algorithms. Zbl 1196.11169
Schoof, René
2008
Trace forms of $$G$$-Galois algebras in virtual cohomological dimension 1 and 2. Zbl 1069.12004
Bayer-Fluckiger, Eva; Monsurrò, Marina; Parimala, R.; Schoof, René
2004
Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein. Zbl 1116.11310
Lario, Joan-C.; Schoof, René
2002
The structure of the minus class groups of abelian number fields. Zbl 0719.11074
Schoof, René
1990
Quadratic fields and factorization. Zbl 0527.12003
Schoof, R. J.
1982
On the modular curve $$X_0(23)$$. Zbl 1317.14098
Schoof, René
2012
A refined counter-example to the support conjecture for abelian varieties. Zbl 1097.14036
Larsen, Michael; Schoof, René
2006
Number fields and function fields – two parallel worlds. Zbl 1078.11002
van der Geer, Gerard (ed.); Moonen, Ben (ed.); Schoof, René (ed.)
2005
Homophonic quotients of free groups. Zbl 0818.20033
Mestre, Jean-François; Schoof, René; Washington, Lawrence; Zagier, Don
1993
Cohomology of class groups of cyclotomic fields; an application to Morse- Smale diffeomorphisms. Zbl 0651.12004
Schoof, René
1988
Papers from the conference 21st Journées Arithmétiques held at the Università Lateranense, Rome, July 12–16, 2001. Zbl 1041.11500
Schoof, René (ed.); Talamanca, Valerio (ed.)
2001
The automorphism group of the non-split Cartan modular curve of level 11. Zbl 1330.14049
Dose, Valerio; Fernández, Julio; González, Josep; Schoof, René
2014
Semistable abelian varieties with good reduction outside 15. Zbl 1323.11040
Schoof, René
2012
Integral points of a modular curve of level 11. Zbl 1292.11057
Schoof, René; Tzanakis, Nikos
2012
On the modular curve $$X_0(23)$$. Zbl 1317.14098
Schoof, René
2012
Visibility of ideal classes. Zbl 1226.11123
Schoof, René; Washington, Lawrence C.
2010
Computing Arakelov class groups. Zbl 1188.11076
Schoof, René
2008
Catalan’s conjecture. Zbl 1186.11018
Schoof, René
2008
Four primality testing algorithms. Zbl 1196.11169
Schoof, René
2008
A refined counter-example to the support conjecture for abelian varieties. Zbl 1097.14036
Larsen, Michael; Schoof, René
2006
Abelian varieties over $$\mathbb Q$$ with bad reduction in one prime only. Zbl 1173.11333
Schoof, René
2005
Number fields and function fields – two parallel worlds. Zbl 1078.11002
van der Geer, Gerard (ed.); Moonen, Ben (ed.); Schoof, René (ed.)
2005
Trace forms of $$G$$-Galois algebras in virtual cohomological dimension 1 and 2. Zbl 1069.12004
Bayer-Fluckiger, Eva; Monsurrò, Marina; Parimala, R.; Schoof, René
2004
Class numbers of real cyclotomic fields of prime conductor. Zbl 1052.11071
Schoof, René
2003
Abelian varieties over cyclotomic fields with good reduction everywhere. Zbl 1058.11038
Schoof, René
2003
Some computations with Hecke rings and deformation rings. With an appendix by Amod Agashe and William Stein. Zbl 1116.11310
Lario, Joan-C.; Schoof, René
2002
Papers from the conference 21st Journées Arithmétiques held at the Università Lateranense, Rome, July 12–16, 2001. Zbl 1041.11500
Schoof, René (ed.); Talamanca, Valerio (ed.)
2001
Effectivity of Arakelov divisors and the theta divisor of a number field. Zbl 1030.11063
van der Geer, Gerard; Schoof, René
2000
Minus class groups of the fields of the $$l$$-th roots of unity. Zbl 0902.11043
Schoof, René
1998
The support problem and its elliptic analogue. Zbl 0922.11086
Corrales-Rodrigáñez, Capi; Schoof, René
1997
Criteria for complete intersections. Zbl 0903.13003
De Smit, Bart; Rubin, Karl; Schoof, René
1997
Beppo Levi and the arithmetic of elliptic curves. Zbl 0849.01036
Schappacher, Norbert; Schoof, René
1996
Counting points on elliptic curves over finite fields. Zbl 0852.11073
Schoof, René
1995
Computing Iwasawa modules of real quadratic number fields. Zbl 0840.11043
Kraft, James S.; Schoof, René
1995
Families of curves and weight distributions of codes. Zbl 0854.11072
Schoof, René
1995
Homophonic quotients of free groups. Zbl 0818.20033
Mestre, Jean-François; Schoof, René; Washington, Lawrence; Zagier, Don
1993
Algebraic curves over $${\mathbb{F}}_ 2$$ with many rational points. Zbl 0762.11026
Schoof, René
1992
Weight formulas for ternary Melas codes. Zbl 0768.94017
van der Geer, Gerard; Schoof, René; van der Vlugt, Marcel
1992
Hecke operators and the weight distributions of certain codes. Zbl 0729.11065
Schoof, René; van der Vlugt, Marcel
1991
The exponents of the groups of points on the reductions of an elliptic curve. Zbl 0726.14023
Schoof, René
1991
The structure of the minus class groups of abelian number fields. Zbl 0719.11074
Schoof, René
1990
Quintic polynomials and real cyclotomic fields with large class numbers. Zbl 0649.12007
Schoof, René; Washington, Lawrence C.
1988
Cohomology of class groups of cyclotomic fields; an application to Morse- Smale diffeomorphisms. Zbl 0651.12004
Schoof, René
1988
Nonsingular plane cubic curves over finite fields. Zbl 0632.14021
Schoof, René
1987
Primitive normal bases for finite fields. Zbl 0615.12023
Lenstra, H. W. jun.; Schoof, R. J.
1987
Infinite class field towers of quadratic fields. Zbl 0589.12011
Schoof, René
1986
Elliptic curves over finite fields and the computation of square roots mod p. Zbl 0579.14025
Schoof, René
1985
Class groups of complex quadratic fields. Zbl 0516.12002
Schoof, R. J.
1983
Quadratic fields and factorization. Zbl 0527.12003
Schoof, R. J.
1982
all top 5

#### Cited by 671 Authors

 12 Sutherland, Andrew V. 11 Schoof, René 10 Ichimura, Humio 9 Maire, Christian 9 Miret, Josep M. 8 Shparlinski, Igor E. 7 Schost, Éric 6 Fan, Shuqin 6 Gras, Georges 6 Morain, François 6 Sumida-Takahashi, Hiroki 5 Banaszak, Grzegorz 5 Bröker, Reinier 5 Hachenberger, Dirk 5 Han, Wenbao 5 Kapetanakis, Giorgos 5 Lercier, Reynald 5 Tran, Ha Thanh Nguyen 5 Vanstone, Scott Alexander 5 von zur Gathen, Joachim 4 Brumer, Armand 4 Cohen, Stephen D. 4 Cornacchia, Pietro 4 Couveignes, Jean-Marc 4 Ezome, Tony 4 Gaudry, Pierrick 4 Huang, Ming-Deh A. 4 Koblitz, Neal I. 4 Kramer, Kenneth B. 4 Krasoń, Piotr 4 Lauder, Alan G. B. 4 Lauter, Kristin Estella 4 Menezes, Alfred J. 4 Moreno, Ramiro 4 Pujolàs, Jordi 4 Robert, Damien 4 Top, Jaap 4 Valls, Magda 4 van der Vlugt, Marcel 4 Vlǎduţ, Sergei Georgievich 4 Xing, Chaoping 3 Barańczuk, Stefan 3 Bayer-Fluckiger, Eva 3 Bisson, Gaetan 3 De Feo, Luca 3 Dieulefait, Luis Victor 3 Doliskani, Javad 3 Farashahi, Reza Rezaeian 3 Feng, Rongquan 3 Fieker, Claus 3 Fukuda, Takashi 3 Gaál, István 3 Gajda, Wojciech 3 Güneri, Cem 3 Hajir, Farshid 3 James, Kevin 3 Kontogeorgis, Aristides I. 3 Lachaud, Gilles 3 Lubicz, David 3 McGuire, Gary 3 Miller, John C. 3 Moisio, Marko J. 3 Nguyen Quang Do, Thong 3 Pomerance, Carl Bernard 3 Reis, Lucas 3 Satoh, Takakazu 3 Scholl, Travis 3 Silverman, Joseph Hillel 3 Smith, Ethan 3 Taya, Hisao 3 Tena Ayuso, Juan Gabriel 3 Thaine, Francisco 3 Valera, Javier 3 Van der Geer, Gerard 3 Voloch, José Felipe 3 Wake, Preston 3 Wan, Daqing 3 Wu, Hongfeng 3 Xiong, Maosheng 3 Zarkhin, Yuriĭ Gennad’evich 2 Abelard, Simon 2 Achter, Jeffrey D. 2 Agathocleous, Eleni 2 Agnew, Gordon B. 2 Anju 2 Bach, Eric 2 Bartoli, Daniele 2 Bekker, Boris Mikhaĭlovich 2 Belabas, Karim 2 Blake, Ian F. 2 Bostan, Alin 2 Bruen, Aiden A. 2 Cao, Xiwang 2 Deng, Yingpu 2 Dose, Valerio 2 Elia, Michele 2 Elkies, Noam David 2 Feng, Keqin 2 Ferri, Stefania 2 Flori, Jean-Pierre ...and 571 more Authors
all top 5

#### Cited in 134 Serials

 68 Mathematics of Computation 68 Journal of Number Theory 50 Finite Fields and their Applications 23 Journal de Théorie des Nombres de Bordeaux 21 LMS Journal of Computation and Mathematics 17 Designs, Codes and Cryptography 11 Journal of Symbolic Computation 11 Journal of Cryptology 11 Applicable Algebra in Engineering, Communication and Computing 10 Proceedings of the American Mathematical Society 9 International Journal of Number Theory 8 Journal of Algebra 8 Transactions of the American Mathematical Society 8 The Ramanujan Journal 7 Rocky Mountain Journal of Mathematics 7 Manuscripta Mathematica 6 Discrete Mathematics 6 Acta Arithmetica 6 Duke Mathematical Journal 6 Journal of Pure and Applied Algebra 6 Experimental Mathematics 5 Annales de l’Institut Fourier 5 Mathematische Annalen 5 Proceedings of the Japan Academy. Series A 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Bulletin of the Australian Mathematical Society 4 Compositio Mathematica 4 Journal of Complexity 4 Computational Complexity 4 Foundations of Computational Mathematics 3 Communications in Algebra 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 3 Archiv der Mathematik 3 Functiones et Approximatio. Commentarii Mathematici 3 Mathematische Zeitschrift 3 Nagoya Mathematical Journal 3 Osaka Journal of Mathematics 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 European Journal of Combinatorics 3 Bulletin of the American Mathematical Society. New Series 3 Journal of Discrete Mathematical Sciences & Cryptography 3 Journal of Algebra and its Applications 3 Advances in Mathematics of Communications 3 Cryptography and Communications 3 Science China. Mathematics 2 Discrete Applied Mathematics 2 Mathematical Notes 2 Advances in Mathematics 2 Applied Mathematics and Computation 2 Inventiones Mathematicae 2 Journal of Combinatorial Theory. Series A 2 Mathematika 2 Results in Mathematics 2 Theoretical Computer Science 2 Tohoku Mathematical Journal. Second Series 2 Acta Applicandae Mathematicae 2 Revista Matemática Iberoamericana 2 Applied Mathematics Letters 2 Journal of the American Mathematical Society 2 Linear Algebra and its Applications 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 St. Petersburg Mathematical Journal 2 Annales Mathématiques Blaise Pascal 2 Journal of Applied Mathematics and Computing 2 Journal of Mathematical Cryptology 2 Asian-European Journal of Mathematics 2 JSIAM Letters 2 Research in Number Theory 1 American Mathematical Monthly 1 Archive for History of Exact Sciences 1 Computers & Mathematics with Applications 1 Information Processing Letters 1 Lithuanian Mathematical Journal 1 Moscow University Mathematics Bulletin 1 Reviews of Modern Physics 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Illinois Journal of Mathematics 1 Information Sciences 1 Publications Mathématiques 1 Journal of Computational and Applied Mathematics 1 Journal of Computer and System Sciences 1 Journal of the Mathematical Society of Japan 1 Journal für die Reine und Angewandte Mathematik 1 Mathematics and Computers in Simulation 1 Mathematische Nachrichten 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Tokyo Journal of Mathematics 1 Advances in Applied Mathematics 1 Combinatorica 1 Chinese Annals of Mathematics. Series B 1 Algorithmica 1 Information and Computation 1 Mathematical and Computer Modelling 1 Journal of the Ramanujan Mathematical Society 1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série ...and 34 more Serials
all top 5

#### Cited in 33 Fields

 510 Number theory (11-XX) 216 Algebraic geometry (14-XX) 103 Information and communication theory, circuits (94-XX) 36 Field theory and polynomials (12-XX) 33 Computer science (68-XX) 19 Group theory and generalizations (20-XX) 13 Combinatorics (05-XX) 12 Geometry (51-XX) 7 Commutative algebra (13-XX) 6 $$K$$-theory (19-XX) 6 Special functions (33-XX) 5 Numerical analysis (65-XX) 4 History and biography (01-XX) 3 Mathematical logic and foundations (03-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Associative rings and algebras (16-XX) 3 Quantum theory (81-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Topological groups, Lie groups (22-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Probability theory and stochastic processes (60-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 General and overarching topics; collections (00-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Convex and discrete geometry (52-XX) 1 Manifolds and cell complexes (57-XX) 1 Statistics (62-XX) 1 Fluid mechanics (76-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX)

#### Wikidata Timeline

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