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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: 39 Publications since 1989, including 1 Book
Reviewing Activity: 89 Reviews
Co-Authors: 7 Co-Authors with 20 Joint Publications
68 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

32 Publications have been cited 222 times in 133 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
31
1990
On a question of B. Mazur. (Sur une question de B. Mazur.) Zbl 0773.14017
Kraus, A.; Oesterlé, J.
26
1992
Effective upper bounds for the generalized Fermat equation. (Majorations effectives pour l’équation de Fermat généralisée.) Zbl 0908.11017
Kraus, Alain
25
1997
On the equation \(a^3+ b^3= c^p\). (Sur l’équation \(a^3+ b^3= c^p\).) Zbl 0923.11054
Kraus, Alain
17
1998
Fermat curves: results and problems. (Courbes de Fermat: résultats et problèmes.) Zbl 1125.11038
Halberstadt, Emmanuel; Kraus, Alain
14
2002
Semi-stable elliptic curves and quadratic fields. (Courbes elliptiques semi-stables et corps quadratiques.) Zbl 0865.11050
Kraus, Alain
12
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
11
1995
On the modular curve \(X_E(7)\). (Sur la courbe modulaire \(X_E(7)\).) Zbl 1050.11056
Halberstadt, Emmanuel; Kraus, Alain
9
2003
On the equation \(x^p+y^q=z^r\): a survey. Zbl 0939.11016
Kraus, Alain
9
1999
Semistable elliptic curves over number fields. (Courbes elliptiques semi-stables sur les corps de nombres.) Zbl 1145.11043
Kraus, Alain
8
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.
7
2006
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
5
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
5
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
5
2002
Class field theory, Diophantine analysis and the asymptotic Fermat’s last theorem. Zbl 1450.11023
Freitas, Nuno; Kraus, Alain; Siksek, Samir
5
2020
On the modular curves \(Y_E(7)\). Zbl 1042.11034
Halberstadt, Emmanuel; Kraus, Alain
4
2000
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
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
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
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
3
2016
The Fermat theorem over \(\mathbb Q(\sqrt{5})\). (Sur le théorème de Fermat sur \(\mathbb Q(\sqrt{5})\).) Zbl 1381.11025
Kraus, Alain
2
2015
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 \(p\)-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
2
1999
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
2
2020
The unit equation over cyclic number fields of prime degree. Zbl 07480698
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
Fermat equation and inert primes. (Équation de Fermat et nombres premiers inertes.) Zbl 1390.11066
Kraus, Alain
1
2015
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
On asymptotic Fermat over \(\mathbb{Z}_p\)-extensions of \(\mathbb{Q}\). Zbl 1492.11073
Freitas, Nuno; Kraus, Alain; Siksek, Samir
1
2020
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
The unit equation over cyclic number fields of prime degree. Zbl 07480698
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
5
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
2
2020
On asymptotic Fermat over \(\mathbb{Z}_p\)-extensions of \(\mathbb{Q}\). Zbl 1492.11073
Freitas, Nuno; Kraus, Alain; Siksek, Samir
1
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
3
2016
The Fermat theorem over \(\mathbb Q(\sqrt{5})\). (Sur le théorème de Fermat sur \(\mathbb Q(\sqrt{5})\).) Zbl 1381.11025
Kraus, Alain
2
2015
Fermat equation and inert primes. (Équation de Fermat et nombres premiers inertes.) Zbl 1390.11066
Kraus, Alain
1
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
Semistable elliptic curves over number fields. (Courbes elliptiques semi-stables sur les corps de nombres.) Zbl 1145.11043
Kraus, Alain
8
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.
7
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
9
2003
Fermat curves: results and problems. (Courbes de Fermat: résultats et problèmes.) Zbl 1125.11038
Halberstadt, Emmanuel; Kraus, Alain
14
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
5
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
5
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
9
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
2
1999
On the equation \(a^3+ b^3= c^p\). (Sur l’équation \(a^3+ b^3= c^p\).) Zbl 0923.11054
Kraus, Alain
17
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
25
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
5
1997
Semi-stable elliptic curves and quadratic fields. (Courbes elliptiques semi-stables et corps quadratiques.) Zbl 0865.11050
Kraus, Alain
12
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
11
1995
On a question of B. Mazur. (Sur une question de B. Mazur.) Zbl 0773.14017
Kraus, A.; Oesterlé, J.
26
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
31
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 110 Authors

22 Siksek, Samir
19 Freitas, Nuno
16 Kraus, Alain
14 Bennett, Michael A.
8 Billerey, Nicolas
7 Chen, Imin
6 Dieulefait, Luis Victor
4 Dahmen, Sander R.
4 Dokchitser, Tim
4 Mignotte, Maurice
3 Cremona, John E.
3 Dąbrowski, Andrzej Bogdan
3 Dokchitser, Vladimir
3 Fisher, Tom A.
3 Luca, Florian
3 Patel, Vandita
3 Pintér, Ákos
3 Ţurcaş, George Cătălin
2 Anni, Samuele
2 Bilu, Yuri F.
2 Bugeaud, Yann
2 Chałupka, Karolina
2 Chrétien, P.
2 Coppola, Nirvana
2 Győry, Kálmán
2 Hajdu, Lajos
2 Halberstadt, Emmanuel
2 Jones, Nathan A.
2 Lorenzo García, Elisa
2 Lozano-Robledo, Álvaro
2 Murty, Maruti Ram
2 Parent, Pierre
2 Reynolds, Jonathan
2 Silverberg, Alice
2 Sinha, Kaneenika
2 Soydan, Gokhan
2 Stoll, Michael
2 Togbé, Alain
2 Yoshikawa, Sho
2 Zarkhin, Yuriĭ Gennad’evich
1 Abu Muriefah, Fadwa S.
1 Barrios, Alexander J.
1 Bhargava, Manjul
1 Bisatt, Matthew
1 Bruni, Carmen
1 Cai, Tianxin
1 Cha, Byungchul
1 Chen, Deyi
1 Chen, Zexiang
1 Cojocaru, Alina Carmen
1 Danielson, Lynda
1 Das, Pranabesh
1 David, Agnès
1 Fein, Burton
1 Fité, Francesc
1 Gassert, Thomas Alden
1 Gherga, Adela
1 Gillibert, Jean
1 González-Jiménez, Enrique
1 Hidalgo, Rubén Antonio
1 Jarvis, Frazer
1 Kara, Yasemin
1 Kida, Masanari
1 Kontogeorgis, Aristides I.
1 Koutsianas, Angelos
1 Kovács, Tünde
1 Laishram, Shanta
1 Laradji, Abdallah
1 Le Hung, Bao V.
1 Le, Maohua
1 Lee, Yoonjin
1 Levin, Aaron
1 Leyton-Alvarez, Maximiliano
1 Lorenzini, Dino J.
1 Martin, Greg
1 Matignon, Michel
1 Mazur, Barry
1 Meekin, Paul
1 Melninkas, Lukas
1 Merel, Loïc
1 Michaud-Jacobs, Philippe
1 Mihăilescu, Preda
1 Mutlu, Elif Kızıldere
1 Najman, Filip
1 Naskrȩcki, Bartosz
1 Noubissie, Armand
1 Ozman, Ekin
1 Pacetti, Ariel
1 Paramantzoglou, Panagiotis A.
1 Peaucelle, Baptiste
1 Philip, Séverin
1 Poonen, Bjorn
1 Prickett, M.
1 Roy, Manami
1 Rubin, Karl Cooper
1 Sabitova, Maria
1 Saradha, N.
1 Schaefer, Edward F.
1 Shankar, Arul
1 Silverman, Joseph Hillel
...and 10 more Authors
all top 5

Cited in 46 Serials

23 Journal of Number Theory
11 International Journal of Number Theory
6 Bulletin of the Australian Mathematical Society
6 Journal de Théorie des Nombres de Bordeaux
5 Mathematics of Computation
5 Compositio Mathematica
5 Transactions of the American Mathematical Society
5 Algebra & Number Theory
4 Acta Arithmetica
4 Mathematische Zeitschrift
4 Proceedings of the American Mathematical Society
3 Mathematische Annalen
3 Annals of Mathematics. Second Series
3 LMS Journal of Computation and Mathematics
3 Research in Number Theory
2 Mathematical Proceedings of the Cambridge Philosophical Society
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 Mathematika
2 Indagationes Mathematicae. New Series
2 Experimental Mathematics
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 European Journal of Mathematics
1 Advances in Mathematics
1 Annales de l’Institut Fourier
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 Boletim da Sociedade Portuguesa de Matemática
1 Revista Matemática Iberoamericana
1 Elemente der Mathematik
1 Journal of Mathematical Sciences (New York)
1 Annales Mathématiques Blaise Pascal
1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
1 Central European Journal of Mathematics
1 Mediterranean Journal of Mathematics
1 Annales Mathématiques du Québec
1 Research in the Mathematical Sciences
1 Bulletin of the Hellenic Mathematical Society

Citations by Year