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Author ID: kraus.alain Recent zbMATH articles by "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

Publications by Year

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 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

Citations by Year