Edit Profile (opens in new tab) Kraus, Alain Co-Author Distance Author ID: kraus.alain Published as: Kraus, Alain; Kraus, A. External Links: MGP Documents Indexed: 42 Publications since 1989, including 1 Book and 3 Additional arXiv Preprints Reviewing Activity: 89 Reviews Co-Authors: 7 Co-Authors with 22 Joint Publications 77 Co-Co-Authors all top 5 Co-Authors 20 single-authored 9 Freitas, Nuno 8 Halberstadt, Emmanuel 6 Siksek, Samir 2 Bernardi, Dominique 2 Cali, Élie 1 Ivorra, Wilfrid 1 Oesterlé, Joseph all top 5 Serials 5 Acta Arithmetica 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Algebra & Number Theory 2 Bulletin of the Australian Mathematical Society 2 Canadian Journal of Mathematics 2 Mathematische Annalen 2 Experimental Mathematics 2 Annales Mathématiques Blaise Pascal 2 International Journal of Number Theory 1 Mathematics of Computation 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Canadian Mathematical Bulletin 1 Compositio Mathematica 1 Dissertationes Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Journal of Number Theory 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Memoirs of the American Mathematical Society 1 Proceedings of the Japan Academy. Series A 1 Journal de Théorie des Nombres de Bordeaux 1 The Ramanujan Journal 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Annales Mathématiques du Québec Fields 42 Number theory (11-XX) 12 Algebraic geometry (14-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 33 Publications have been cited 278 times in 159 Documents Cited by ▼ Year ▼ On the failure of semistability of elliptic curves with additive reduction. (Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive.) Zbl 0792.14014 Kraus, Alain 43 1990 On a question of B. Mazur. (Sur une question de B. Mazur.) Zbl 0773.14017 Kraus, A.; Oesterlé, J. 31 1992 Effective upper bounds for the generalized Fermat equation. (Majorations effectives pour l’équation de Fermat généralisée.) Zbl 0908.11017 Kraus, Alain 28 1997 Fermat curves: results and problems. (Courbes de Fermat: résultats et problèmes.) Zbl 1125.11038 Halberstadt, Emmanuel; Kraus, Alain 20 2002 On the equation \(a^3+ b^3= c^p\). (Sur l’équation \(a^3+ b^3= c^p\).) Zbl 0923.11054 Kraus, Alain 20 1998 A remark on the torsion points of elliptic curves. (Une remarque sur les points de torsion des courbes elliptiques.) Zbl 0862.11037 Kraus, Alain 14 1995 Semi-stable elliptic curves and quadratic fields. (Courbes elliptiques semi-stables et corps quadratiques.) Zbl 0865.11050 Kraus, Alain 13 1996 On the equation \(x^p+y^q=z^r\): a survey. Zbl 0939.11016 Kraus, Alain 11 1999 On the modular curve \(X_E(7)\). (Sur la courbe modulaire \(X_E(7)\).) Zbl 1050.11056 Halberstadt, Emmanuel; Kraus, Alain 11 2003 Semistable elliptic curves over number fields. (Courbes elliptiques semi-stables sur les corps de nombres.) Zbl 1145.11043 Kraus, Alain 9 2007 Some results on the equations \(ax^p+by^p= cz^2\). (Quelques résultats sur les équations \(ax^p+by^p= cz^2\).) Zbl 1139.11021 Ivorra, W.; Kraus, A. 8 2006 Class field theory, Diophantine analysis and the asymptotic Fermat’s last theorem. Zbl 1450.11023 Freitas, Nuno; Kraus, Alain; Siksek, Samir 8 2020 Determination of weight and conductor associated to representations of \(p\)-torsion points of an elliptic curve. (Détermination du poids et du conducteur associés aux représentations des points de \(p\)-torsion d’une courbe elliptique.) Zbl 0881.11053 Kraus, Alain 6 1997 Une question sur les équations \(x^m - y^m = Rz^n\). (A question on the equations \(x^m - y^m = Rz^n\)). Zbl 1004.11016 Kraus, Alain 6 2002 On the \(p\)-different of the field of the points of \(\ell\) torsion of elliptic curves, \(\ell\neq p\). (Sur la \(p\)-différente du corps des points de \(\ell\)-torsion des courbes elliptiques, \(\ell\neq p\).) Zbl 1052.11040 Cali, Élie; Kraus, Alain 6 2002 An application of the symplectic argument to some Fermat-type equations. (Une application du critère symplectique à quelques équations de Fermat.) Zbl 1423.11072 Freitas, Nuno; Kraus, Alain 5 2016 On the modular curves \(Y_E(7)\). Zbl 1042.11034 Halberstadt, Emmanuel; Kraus, Alain 4 2000 On the symplectic type of isomorphisms of the \(p\)-torsion of elliptic curves. Zbl 1519.11002 Freitas, Nuno; Kraus, Alain 4 2022 Quelques remarques à propos des invariants \(c_ 4\), \(c_ 6\) et \(\Delta\) d’une courbe elliptique. (Some remarks about the invariants \(c_ 4\), \(c_ 6\) and \(\Delta\) of an elliptic curve). Zbl 0628.14024 Kraus, Alain 3 1989 On the \(p\)-different of the field of the \(p\)-division points of elliptic curves. (Sur la \(p\)-différente du corps des points de \(p\)-torsion des courbes elliptiques.) Zbl 0938.11028 Kraus, Alain 3 1999 About the 7-torsion modules of points of a family of elliptic curves. (Sur les modules des points de 7-torsion d’une famille de courbes elliptiques.) Zbl 0853.11046 Kraus, Alain 3 1996 The Fermat theorem over \(\mathbb Q(\sqrt{5})\). (Sur le théorème de Fermat sur \(\mathbb Q(\sqrt{5})\).) Zbl 1381.11025 Kraus, Alain 3 2015 On asymptotic Fermat over \(\mathbb{Z}_p\)-extensions of \(\mathbb{Q}\). Zbl 1492.11073 Freitas, Nuno; Kraus, Alain; Siksek, Samir 3 2020 Fermat’s theorem over some totally real number fields. (Le théorème de Fermat sur certains corps de nombres totalement réels.) Zbl 1441.11063 Kraus, Alain 3 2019 On the degree of the \(p\)-torsion field of elliptic curves over \(\mathbb{Q}_\ell\) for \(\ell \neq p\). Zbl 1448.11103 Freitas, Nuno; Kraus, Alain 3 2020 On torsion modules of elliptic curves. (Sur les modules de torsion des courbes elliptiques.) Zbl 1042.11518 Halberstadt, Emmanuel; Kraus, Alain 2 1998 A Lebesgue’s conjecture. (Une conjecture de Lebesgue.) Zbl 1065.11046 Halberstadt, Emmanuel; Kraus, Alain 2 2004 On the Galois comparison of the torsion points of elliptic curves. (Sur la comparaison galoisienne des points de torsion des courbes elliptiques.) Zbl 0857.11027 Halberstadt, Emmanuel; Kraus, Alain 1 1996 On the equations \(a^ p+b^ p+15c^ p=0\) and \(a^ p+3b^ p+5c^ p=0\). (Sur les équations \(a^ p+b^ p+15c^ p=0\) et \(a^ p+3b^ p+5c^ p=0\).) Zbl 0855.11015 Kraus, Alain 1 1996 Remarks on the first case of Fermat’s theorem over number fields. (Remarques sur le premier cas du théorème de Fermat sur les corps de nombres.) Zbl 1364.11082 Kraus, Alain 1 2015 Fermat equation and inert primes. (Équation de Fermat et nombres premiers inertes.) Zbl 1390.11066 Kraus, Alain 1 2015 The unit equation over cyclic number fields of prime degree. Zbl 1497.11267 Freitas, Nuno; Kraus, Alain; Siksek, Samir 1 2021 Quartic points on the Fermat quintic. (Points quartiques sur la quintique de Fermat.) Zbl 1429.11063 Kraus, Alain 1 2018 On the symplectic type of isomorphisms of the \(p\)-torsion of elliptic curves. Zbl 1519.11002 Freitas, Nuno; Kraus, Alain 4 2022 The unit equation over cyclic number fields of prime degree. Zbl 1497.11267 Freitas, Nuno; Kraus, Alain; Siksek, Samir 1 2021 Class field theory, Diophantine analysis and the asymptotic Fermat’s last theorem. Zbl 1450.11023 Freitas, Nuno; Kraus, Alain; Siksek, Samir 8 2020 On asymptotic Fermat over \(\mathbb{Z}_p\)-extensions of \(\mathbb{Q}\). Zbl 1492.11073 Freitas, Nuno; Kraus, Alain; Siksek, Samir 3 2020 On the degree of the \(p\)-torsion field of elliptic curves over \(\mathbb{Q}_\ell\) for \(\ell \neq p\). Zbl 1448.11103 Freitas, Nuno; Kraus, Alain 3 2020 Fermat’s theorem over some totally real number fields. (Le théorème de Fermat sur certains corps de nombres totalement réels.) Zbl 1441.11063 Kraus, Alain 3 2019 Quartic points on the Fermat quintic. (Points quartiques sur la quintique de Fermat.) Zbl 1429.11063 Kraus, Alain 1 2018 An application of the symplectic argument to some Fermat-type equations. (Une application du critère symplectique à quelques équations de Fermat.) Zbl 1423.11072 Freitas, Nuno; Kraus, Alain 5 2016 The Fermat theorem over \(\mathbb Q(\sqrt{5})\). (Sur le théorème de Fermat sur \(\mathbb Q(\sqrt{5})\).) Zbl 1381.11025 Kraus, Alain 3 2015 Remarks on the first case of Fermat’s theorem over number fields. (Remarques sur le premier cas du théorème de Fermat sur les corps de nombres.) Zbl 1364.11082 Kraus, Alain 1 2015 Fermat equation and inert primes. (Équation de Fermat et nombres premiers inertes.) Zbl 1390.11066 Kraus, Alain 1 2015 Semistable elliptic curves over number fields. (Courbes elliptiques semi-stables sur les corps de nombres.) Zbl 1145.11043 Kraus, Alain 9 2007 Some results on the equations \(ax^p+by^p= cz^2\). (Quelques résultats sur les équations \(ax^p+by^p= cz^2\).) Zbl 1139.11021 Ivorra, W.; Kraus, A. 8 2006 A Lebesgue’s conjecture. (Une conjecture de Lebesgue.) Zbl 1065.11046 Halberstadt, Emmanuel; Kraus, Alain 2 2004 On the modular curve \(X_E(7)\). (Sur la courbe modulaire \(X_E(7)\).) Zbl 1050.11056 Halberstadt, Emmanuel; Kraus, Alain 11 2003 Fermat curves: results and problems. (Courbes de Fermat: résultats et problèmes.) Zbl 1125.11038 Halberstadt, Emmanuel; Kraus, Alain 20 2002 Une question sur les équations \(x^m - y^m = Rz^n\). (A question on the equations \(x^m - y^m = Rz^n\)). Zbl 1004.11016 Kraus, Alain 6 2002 On the \(p\)-different of the field of the points of \(\ell\) torsion of elliptic curves, \(\ell\neq p\). (Sur la \(p\)-différente du corps des points de \(\ell\)-torsion des courbes elliptiques, \(\ell\neq p\).) Zbl 1052.11040 Cali, Élie; Kraus, Alain 6 2002 On the modular curves \(Y_E(7)\). Zbl 1042.11034 Halberstadt, Emmanuel; Kraus, Alain 4 2000 On the equation \(x^p+y^q=z^r\): a survey. Zbl 0939.11016 Kraus, Alain 11 1999 On the \(p\)-different of the field of the \(p\)-division points of elliptic curves. (Sur la \(p\)-différente du corps des points de \(p\)-torsion des courbes elliptiques.) Zbl 0938.11028 Kraus, Alain 3 1999 On the equation \(a^3+ b^3= c^p\). (Sur l’équation \(a^3+ b^3= c^p\).) Zbl 0923.11054 Kraus, Alain 20 1998 On torsion modules of elliptic curves. (Sur les modules de torsion des courbes elliptiques.) Zbl 1042.11518 Halberstadt, Emmanuel; Kraus, Alain 2 1998 Effective upper bounds for the generalized Fermat equation. (Majorations effectives pour l’équation de Fermat généralisée.) Zbl 0908.11017 Kraus, Alain 28 1997 Determination of weight and conductor associated to representations of \(p\)-torsion points of an elliptic curve. (Détermination du poids et du conducteur associés aux représentations des points de \(p\)-torsion d’une courbe elliptique.) Zbl 0881.11053 Kraus, Alain 6 1997 Semi-stable elliptic curves and quadratic fields. (Courbes elliptiques semi-stables et corps quadratiques.) Zbl 0865.11050 Kraus, Alain 13 1996 About the 7-torsion modules of points of a family of elliptic curves. (Sur les modules des points de 7-torsion d’une famille de courbes elliptiques.) Zbl 0853.11046 Kraus, Alain 3 1996 On the Galois comparison of the torsion points of elliptic curves. (Sur la comparaison galoisienne des points de torsion des courbes elliptiques.) Zbl 0857.11027 Halberstadt, Emmanuel; Kraus, Alain 1 1996 On the equations \(a^ p+b^ p+15c^ p=0\) and \(a^ p+3b^ p+5c^ p=0\). (Sur les équations \(a^ p+b^ p+15c^ p=0\) et \(a^ p+3b^ p+5c^ p=0\).) Zbl 0855.11015 Kraus, Alain 1 1996 A remark on the torsion points of elliptic curves. (Une remarque sur les points de torsion des courbes elliptiques.) Zbl 0862.11037 Kraus, Alain 14 1995 On a question of B. Mazur. (Sur une question de B. Mazur.) Zbl 0773.14017 Kraus, A.; Oesterlé, J. 31 1992 On the failure of semistability of elliptic curves with additive reduction. (Sur le défaut de semi-stabilité des courbes elliptiques à réduction additive.) Zbl 0792.14014 Kraus, Alain 43 1990 Quelques remarques à propos des invariants \(c_ 4\), \(c_ 6\) et \(\Delta\) d’une courbe elliptique. (Some remarks about the invariants \(c_ 4\), \(c_ 6\) and \(\Delta\) of an elliptic curve). Zbl 0628.14024 Kraus, Alain 3 1989 all cited Publications top 5 cited Publications all top 5 Cited by 129 Authors 23 Siksek, Samir 21 Freitas, Nuno 16 Bennett, Michael A. 16 Kraus, Alain 9 Billerey, Nicolas 9 Chen, Imin 7 Dieulefait, Luis Victor 4 Dahmen, Sander R. 4 Dokchitser, Tim 4 Mignotte, Maurice 4 Pintér, Ákos 3 Cremona, John E. 3 Dąbrowski, Andrzej Bogdan 3 Dokchitser, Vladimir 3 Fisher, Tom A. 3 Győry, Kálmán 3 Luca, Florian 3 Patel, Vandita 3 Torcomian, Lucas Villagra 3 Ţurcaş, George Cătălin 2 Anni, Samuele 2 Barrios, Alexander J. 2 Bilu, Yuri F. 2 Bugeaud, Yann 2 Chałupka, Karolina 2 Chrétien, Pierre 2 Coppola, Nirvana 2 Das, Pranabesh 2 Hajdu, Lajos 2 Halberstadt, Emmanuel 2 Jones, Nathan A. 2 Kara, Yasemin 2 Kida, Masanari 2 Koutsianas, Angelos 2 Laishram, Shanta 2 Lorenzo García, Elisa 2 Lozano-Robledo, Álvaro 2 Melninkas, Lukas 2 Michaud-Jacobs, Philippe 2 Murty, Maruti Ram 2 Najman, Filip 2 Ozman, Ekin 2 Parent, Pierre 2 Philip, Séverin 2 Poonen, Bjorn 2 Reynolds, Jonathan 2 Roy, Manami 2 Saradha, N. 2 Silverberg, Alice 2 Sinha, Kaneenika 2 Smith, Hanson 2 Soydan, Gokhan 2 Stoll, Michael 2 Togbé, Alain 2 Yoshikawa, Sho 2 Zarkhin, Yuriĭ Gennad’evich 1 Abu Muriefah, Fadwa S. 1 Belabas, Karim 1 Bhargava, Manjul 1 Bisatt, Matthew 1 Bruni, Carmen 1 Cai, Tianxin 1 Česnavičius, Kęstutis 1 Cha, Byungchul 1 Chen, Deyi 1 Chen, Zexiang 1 Cojocaru, Alina Carmen 1 Dainobu, Naoto 1 Danielson, Lynda 1 David, Agnès 1 de La Rochefoucauld, Thomas 1 Dembélé, Lassina 1 Dujella, Andrej 1 Efemwonkieke, Aisosa 1 Fein, Burton 1 Fité, Francesc 1 Frengley, Sam 1 Gassert, Thomas Alden 1 Gherga, Adela 1 Gillibert, Jean 1 González-Jiménez, Enrique 1 Hidalgo, Rubén Antonio 1 Işik, Erman 1 Jarvis, Frazer 1 Kontogeorgis, Aristides I. 1 Kovács, Tünde 1 Kundu, Debanjana 1 Laradji, Abdallah 1 Le Hung, Bao Viet 1 Le, Maohua 1 Lee, Yoonjin 1 Levin, Aaron 1 Leyton-Alvarez, Maximiliano 1 Lin, Wenwen 1 Lorenzini, Dino J. 1 Ma, Wenjun 1 Madriaga, Franco Golfieri 1 Martin, Greg 1 Matignon, Michel 1 Mazur, Barry ...and 29 more Authors all top 5 Cited in 56 Serials 25 Journal of Number Theory 13 International Journal of Number Theory 6 Bulletin of the Australian Mathematical Society 6 Mathematics of Computation 6 Acta Arithmetica 6 Proceedings of the American Mathematical Society 6 Journal de Théorie des Nombres de Bordeaux 6 Algebra & Number Theory 5 Compositio Mathematica 5 Transactions of the American Mathematical Society 4 Mathematische Zeitschrift 4 Research in Number Theory 3 Bulletin of the London Mathematical Society 3 Mathematische Annalen 3 Mathematika 3 Annals of Mathematics. Second Series 3 LMS Journal of Computation and Mathematics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Canadian Journal of Mathematics 2 Duke Mathematical Journal 2 Functiones et Approximatio. Commentarii Mathematici 2 Journal of the London Mathematical Society. Second Series 2 Journal of Pure and Applied Algebra 2 Publicacions Matemàtiques 2 Indagationes Mathematicae. New Series 2 Experimental Mathematics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 European Journal of Mathematics 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Bulletin de la Société Mathématique de France 1 Colloquium Mathematicum 1 Commentarii Mathematici Helvetici 1 Inventiones Mathematicae 1 Journal of Algebra 1 Manuscripta Mathematica 1 Memoirs of the American Mathematical Society 1 Nagoya Mathematical Journal 1 Proceedings of the London Mathematical Society. Third Series 1 Tokyo Journal of Mathematics 1 Boletim da Sociedade Portuguesa de Matemática 1 Revista Matemática Iberoamericana 1 Journal of the Ramanujan Mathematical Society 1 Elemente der Mathematik 1 Journal of Mathematical Sciences (New York) 1 Annales Mathématiques Blaise Pascal 1 The Ramanujan Journal 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Milan Journal of Mathematics 1 Central European Journal of Mathematics 1 Mediterranean Journal of Mathematics 1 Oberwolfach Reports 1 Annales Mathématiques du Québec 1 Research in the Mathematical Sciences 1 Bulletin of the Hellenic Mathematical Society Cited in 4 Fields 157 Number theory (11-XX) 40 Algebraic geometry (14-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) Citations by Year