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Philippon, Patrice

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Author ID: philippon.patrice Recent zbMATH articles by "Philippon, Patrice"
Published as: Philippon, P.; Philippon, Patrice
External Links: MGP
Documents Indexed: 64 Publications since 1980, including 3 Books
Reviewing Activity: 113 Reviews
all top 5

Serials

3 Bulletin of the Australian Mathematical Society
3 Acta Arithmetica
3 Journal of Number Theory
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Annales de l’Institut Fourier
2 Bulletin de la Société Mathématique de France
2 Illinois Journal of Mathematics
2 Inventiones Mathematicae
2 Journal für die Reine und Angewandte Mathematik
2 Comptes Rendus de l’Académie des Sciences. Série I
2 Journal of Algebraic Geometry
1 Rocky Mountain Journal of Mathematics
1 Advances in Mathematics
1 American Journal of Mathematics
1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
1 Commentarii Mathematici Helvetici
1 Publications Mathématiques
1 Journal of the London Mathematical Society. Second Series
1 Mathematische Annalen
1 Comptes Rendus Mathématiques de l’Académie des Sciences
1 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Mémoires de la Société Mathématique de France. Nouvelle Série
1 Notices of the American Mathematical Society
1 Journal de Théorie des Nombres de Bordeaux
1 The Ramanujan Journal
1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique
1 Annals of Mathematics. Second Series
1 Journal of the Institute of Mathematics of Jussieu
1 IMRP. International Mathematics Research Papers
1 International Journal of Number Theory
1 Astérisque
1 Lecture Notes in Mathematics
1 Kyoto Journal of Mathematics

Publications by Year

Citations contained in zbMATH Open

52 Publications have been cited 471 times in 285 Documents Cited by Year
Algebraic independence criteria. Zbl 0615.10044
Philippon, Patrice
55
1986
Lemmes de zéros dans les groupes algébriques commutatifs. (Zero theorems in commutative algebraic groups). Zbl 0617.14001
Philippon, Patrice
54
1986
Sur des hauteurs alternatives. I. (On alternative heights. I). Zbl 0726.14017
Philippon, Patrice
39
1991
On alternative heights. III. Zbl 0878.11025
Philippon, Patrice
28
1995
Arithmetic geometry of toric varieties. Metrics, measures and heights. Zbl 1311.14050
Burgos Gil, José Ignacio; Philippon, Patrice; Sombra, Martín
22
2014
Linear forms in logarithms on commutative algebraic groups. Zbl 0651.10023
Philippon, Patrice; Waldschmidt, Michel
20
1988
Lower bounds for normalized heights of subvarieties of tori. Zbl 1002.11055
David, Sinnou; Philippon, Patrice
17
1999
Introduction to algebraic independence theory. With contributions from F. Amoroso, D. Bertrand, W. D. Brownawell, G. Diaz, M. Laurent, Yu. V. Nesterenko, K. Nishioka, P. Philippon, G. Rémond, D. Roy, M. Waldschmidt. Zbl 0966.11032
Nesterenko, Yu. V. (ed.); Philippon, Patrice (ed.)
14
2001
Minorations des hauteurs normalisées des sous-variétés de variétés abeliennes. II. (Lower bounds for normalized heights of subvarieties of Abelian varieties. II.). Zbl 1030.11026
David, Sinnou; Philippon, Patrice
13
2002
Lower bounds for linear forms in logarithms. Zbl 0659.10037
Philippon, P.; Waldschmidt, M.
13
1988
Algebraic subgroups of commutative algebraic groups. Zbl 0618.14020
Bertrand, Daniel; Philippon, Patrice
13
1988
A methodic approach to the transcendence and algebraic independence of values of analytic functions. Zbl 0901.11026
Philippon, Patrice
11
1997
New zero lemmas in commutative algebraic groups. Zbl 0893.11027
Philippon, Patrice
11
1996
Normalized height of projective toric varieties. Zbl 1147.11033
Philippon, Patrice; Sombra, Martín
10
2008
Regularity and interpolation. Zbl 0962.13014
Chardin, Marc; Philippon, Patrice
10
1999
Algebraic independence and \(K\)-functions. Zbl 0887.11032
Philippon, Patrice
10
1998
Sur des hauteurs alternatives. II (On alternative heights. II). Zbl 0878.11024
Philippon, Patrice
10
1994
Denominateurs dans le theoreme des zeros de Hilbert. (Nominators in Hilbert’s zero theorem). Zbl 0679.13010
Philippon, Patrice
9
1991
Arithmetic positivity on toric varieties. Zbl 1378.14048
Burgos Gil, José Ignacio; Moriwaki, Atsushi; Philippon, Patrice; Sombra, Martín
8
2016
A refinement of the Bernštein-Kušnirenko estimate. Zbl 1155.14037
Philippon, Patrice; Sombra, Martín
8
2008
Abelian varieties and algebraic independence. II: An abelian analogue of the Lindemann-Weierstrass theorem. Zbl 0516.10026
Philippon, P.
8
1983
Simultaneous linear forms in logarithms on commutative algebraic groups. Zbl 0681.10024
Philippon, P.; Waldschmidt, M.
7
1988
Sur les mesures d’indépendance algébrique. (On measures of algebraic independence). Zbl 0567.10034
Philippon, P.
7
1985
Independance algébrique de valeurs de fonctions exponentielles p-adiques. Zbl 0459.10024
Philippon, P.
7
1981
Lower bounds for normalized heights of subvarieties of abelian varieties. Zbl 0899.11027
David, Sinnou; Philippon, Patrice
6
1998
Galois groups and automatic numbers. Zbl 1391.11087
Philippon, Patrice
5
2015
Successive minima of toric height functions. Zbl 1369.14034
Burgos Gil, José Ignacio; Philippon, Patrice; Sombra, Martín
4
2015
Some diophantine aspects of projective toric varieties. Zbl 1153.11029
Philippon, Patrice; Sombra, Martín
4
2008
Algebraic approximations of points in projective spaces. I. Zbl 1096.11504
Philippon, Patrice
4
2000
Critères pour l’indépendance algébrique dans les anneaux diophantiens. (Criteria for algebraic independence in diophantine domains). Zbl 0781.13011
Philippon, Patrice
4
1992
Formes linéaires de logarithmes elliptiques et mesures de transcendance. (Linear forms in elliptic logarithms and transcendence measures). Zbl 0692.10035
Philippon, Patrice; Waldschmidt, Michel
4
1989
Variétés abeliennes et independance algébrique. I. Zbl 0503.10024
Philippon, P.
4
1983
Torsion subvarieties of semi-abelian varieties. Zbl 0972.11059
David, Sinnou; Philippon, Patrice
3
2000
Some remarks on questions of diophantine approximation. Zbl 0927.11040
Philippon, Patrice
3
1999
Measures of approximation of values of analytic functions. Zbl 0938.11038
Philippon, Patrice
3
1999
Mahler’s classification and local distances. Zbl 0799.11019
Philippon, Patrice
3
1994
Polynômes d’interpolation sur \({\mathbb{Z}}\) et \({\mathbb{Z}}[i]\). (Interpolating polynomials on \({\mathbb{Z}}\) and \({\mathbb{Z}}[i])\). Zbl 0701.11023
Philippon, Patrice
3
1990
Effective Nullstellensatz and elimination. Zbl 0743.11036
Philippon, P.
2
1989
Addendum to the text of W. D. Brownawell: “Bounds for the degrees in the Nullstellensatz”. Zbl 0641.14002
Philippon, Patrice
2
1988
Height of varieties over finitely generated fields. Zbl 1358.14021
Gil, José Ignacio Burgos; Philippon, Patrice; Sombra, Martín
1
2016
A Farey tail. Zbl 1351.11016
Philippon, Patrice
1
2012
Functional approximations of curves in projective space. Zbl 1231.11075
Philippon, Patrice
1
2011
Height of toric subschemes and Legendre-Fenchel duality. Zbl 1171.14016
Gil, José Ignacio Burgos; Philippon, Patrice; Sombra, Martín
1
2009
Remark on \(p\)-adic algebraic independence theory. Zbl 1196.11105
Philippon, Patrice
1
2008
Essential minimum and obstruction degrees of subtorus translations. Zbl 1230.11085
Philippon, Patrice; Sombra, Martín
1
2008
Uniform bounds for the number of rational points of certain curves. Zbl 1230.14031
David, Sinnou; Nakamaye, Michael; Philippon, Patrice
1
2007
Lower bounds of normalized heights of subvarieties of powers of elliptic curves. Zbl 1163.11049
David, Sinnou; Philippon, Patrice
1
2007
Une nouvelle majoration pour le nombre de solutions d’un système d’équations polynomiales. Zbl 1128.14039
Philippon, Patrice; Sombra, Martín
1
2007
Diophantine geometry and toric varieties. Zbl 1110.14024
Philippon, Patrice; Sombra, Martín
1
2005
New aspects of transcendence. Zbl 0843.11035
Philippon, Patrice
1
1995
Errata et addenda à “Lemmes de zéros dans les groupes algébriques commutatifs”. (Errata and addenda to: “Zero theorems in commutative algebraic groups”). Zbl 0634.14001
Philippon, Patrice
1
1987
Les nombres transcendants. Zbl 0548.10021
Bertrand, D.; Emsalem, M.; Gramain, F.; Huttner, M.; Langevin, M.; Laurent, M.; Mignotte, M.; Moreau, J.-C.; Philippon, P.; Reyssat, E.; Waldschmidt, M.
1
1984
Arithmetic positivity on toric varieties. Zbl 1378.14048
Burgos Gil, José Ignacio; Moriwaki, Atsushi; Philippon, Patrice; Sombra, Martín
8
2016
Height of varieties over finitely generated fields. Zbl 1358.14021
Gil, José Ignacio Burgos; Philippon, Patrice; Sombra, Martín
1
2016
Galois groups and automatic numbers. Zbl 1391.11087
Philippon, Patrice
5
2015
Successive minima of toric height functions. Zbl 1369.14034
Burgos Gil, José Ignacio; Philippon, Patrice; Sombra, Martín
4
2015
Arithmetic geometry of toric varieties. Metrics, measures and heights. Zbl 1311.14050
Burgos Gil, José Ignacio; Philippon, Patrice; Sombra, Martín
22
2014
A Farey tail. Zbl 1351.11016
Philippon, Patrice
1
2012
Functional approximations of curves in projective space. Zbl 1231.11075
Philippon, Patrice
1
2011
Height of toric subschemes and Legendre-Fenchel duality. Zbl 1171.14016
Gil, José Ignacio Burgos; Philippon, Patrice; Sombra, Martín
1
2009
Normalized height of projective toric varieties. Zbl 1147.11033
Philippon, Patrice; Sombra, Martín
10
2008
A refinement of the Bernštein-Kušnirenko estimate. Zbl 1155.14037
Philippon, Patrice; Sombra, Martín
8
2008
Some diophantine aspects of projective toric varieties. Zbl 1153.11029
Philippon, Patrice; Sombra, Martín
4
2008
Remark on \(p\)-adic algebraic independence theory. Zbl 1196.11105
Philippon, Patrice
1
2008
Essential minimum and obstruction degrees of subtorus translations. Zbl 1230.11085
Philippon, Patrice; Sombra, Martín
1
2008
Uniform bounds for the number of rational points of certain curves. Zbl 1230.14031
David, Sinnou; Nakamaye, Michael; Philippon, Patrice
1
2007
Lower bounds of normalized heights of subvarieties of powers of elliptic curves. Zbl 1163.11049
David, Sinnou; Philippon, Patrice
1
2007
Une nouvelle majoration pour le nombre de solutions d’un système d’équations polynomiales. Zbl 1128.14039
Philippon, Patrice; Sombra, Martín
1
2007
Diophantine geometry and toric varieties. Zbl 1110.14024
Philippon, Patrice; Sombra, Martín
1
2005
Minorations des hauteurs normalisées des sous-variétés de variétés abeliennes. II. (Lower bounds for normalized heights of subvarieties of Abelian varieties. II.). Zbl 1030.11026
David, Sinnou; Philippon, Patrice
13
2002
Introduction to algebraic independence theory. With contributions from F. Amoroso, D. Bertrand, W. D. Brownawell, G. Diaz, M. Laurent, Yu. V. Nesterenko, K. Nishioka, P. Philippon, G. Rémond, D. Roy, M. Waldschmidt. Zbl 0966.11032
Nesterenko, Yu. V. (ed.); Philippon, Patrice (ed.)
14
2001
Algebraic approximations of points in projective spaces. I. Zbl 1096.11504
Philippon, Patrice
4
2000
Torsion subvarieties of semi-abelian varieties. Zbl 0972.11059
David, Sinnou; Philippon, Patrice
3
2000
Lower bounds for normalized heights of subvarieties of tori. Zbl 1002.11055
David, Sinnou; Philippon, Patrice
17
1999
Regularity and interpolation. Zbl 0962.13014
Chardin, Marc; Philippon, Patrice
10
1999
Some remarks on questions of diophantine approximation. Zbl 0927.11040
Philippon, Patrice
3
1999
Measures of approximation of values of analytic functions. Zbl 0938.11038
Philippon, Patrice
3
1999
Algebraic independence and \(K\)-functions. Zbl 0887.11032
Philippon, Patrice
10
1998
Lower bounds for normalized heights of subvarieties of abelian varieties. Zbl 0899.11027
David, Sinnou; Philippon, Patrice
6
1998
A methodic approach to the transcendence and algebraic independence of values of analytic functions. Zbl 0901.11026
Philippon, Patrice
11
1997
New zero lemmas in commutative algebraic groups. Zbl 0893.11027
Philippon, Patrice
11
1996
On alternative heights. III. Zbl 0878.11025
Philippon, Patrice
28
1995
New aspects of transcendence. Zbl 0843.11035
Philippon, Patrice
1
1995
Sur des hauteurs alternatives. II (On alternative heights. II). Zbl 0878.11024
Philippon, Patrice
10
1994
Mahler’s classification and local distances. Zbl 0799.11019
Philippon, Patrice
3
1994
Critères pour l’indépendance algébrique dans les anneaux diophantiens. (Criteria for algebraic independence in diophantine domains). Zbl 0781.13011
Philippon, Patrice
4
1992
Sur des hauteurs alternatives. I. (On alternative heights. I). Zbl 0726.14017
Philippon, Patrice
39
1991
Denominateurs dans le theoreme des zeros de Hilbert. (Nominators in Hilbert’s zero theorem). Zbl 0679.13010
Philippon, Patrice
9
1991
Polynômes d’interpolation sur \({\mathbb{Z}}\) et \({\mathbb{Z}}[i]\). (Interpolating polynomials on \({\mathbb{Z}}\) and \({\mathbb{Z}}[i])\). Zbl 0701.11023
Philippon, Patrice
3
1990
Formes linéaires de logarithmes elliptiques et mesures de transcendance. (Linear forms in elliptic logarithms and transcendence measures). Zbl 0692.10035
Philippon, Patrice; Waldschmidt, Michel
4
1989
Effective Nullstellensatz and elimination. Zbl 0743.11036
Philippon, P.
2
1989
Linear forms in logarithms on commutative algebraic groups. Zbl 0651.10023
Philippon, Patrice; Waldschmidt, Michel
20
1988
Lower bounds for linear forms in logarithms. Zbl 0659.10037
Philippon, P.; Waldschmidt, M.
13
1988
Algebraic subgroups of commutative algebraic groups. Zbl 0618.14020
Bertrand, Daniel; Philippon, Patrice
13
1988
Simultaneous linear forms in logarithms on commutative algebraic groups. Zbl 0681.10024
Philippon, P.; Waldschmidt, M.
7
1988
Addendum to the text of W. D. Brownawell: “Bounds for the degrees in the Nullstellensatz”. Zbl 0641.14002
Philippon, Patrice
2
1988
Errata et addenda à “Lemmes de zéros dans les groupes algébriques commutatifs”. (Errata and addenda to: “Zero theorems in commutative algebraic groups”). Zbl 0634.14001
Philippon, Patrice
1
1987
Algebraic independence criteria. Zbl 0615.10044
Philippon, Patrice
55
1986
Lemmes de zéros dans les groupes algébriques commutatifs. (Zero theorems in commutative algebraic groups). Zbl 0617.14001
Philippon, Patrice
54
1986
Sur les mesures d’indépendance algébrique. (On measures of algebraic independence). Zbl 0567.10034
Philippon, P.
7
1985
Les nombres transcendants. Zbl 0548.10021
Bertrand, D.; Emsalem, M.; Gramain, F.; Huttner, M.; Langevin, M.; Laurent, M.; Mignotte, M.; Moreau, J.-C.; Philippon, P.; Reyssat, E.; Waldschmidt, M.
1
1984
Abelian varieties and algebraic independence. II: An abelian analogue of the Lindemann-Weierstrass theorem. Zbl 0516.10026
Philippon, P.
8
1983
Variétés abeliennes et independance algébrique. I. Zbl 0503.10024
Philippon, P.
4
1983
Independance algébrique de valeurs de fonctions exponentielles p-adiques. Zbl 0459.10024
Philippon, P.
7
1981
all top 5

Cited by 227 Authors

22 Philippon, Patrice
15 Sombra, Martín
10 Roy, Damien
8 Waldschmidt, Michel
7 Amoroso, Francesco
7 David, Sinnou
6 Gaudron, Éric
6 Gubler, Walter Bruno
6 Masser, David William
6 Murty, Maruti Ram
6 Nakamaye, Michael
6 Rémond, Gaël
6 Viada, Evelina
5 Ably, Mohammed
5 Burgos Gil, José Ignacio
5 Li, Wei
5 Pardo, Luis Miguel
5 Tubbs, Robert
4 Bost, Jean-Benoît
4 Boucksom, Sébastien
4 Chen, Huayi
4 D’Andrea, Carlos
4 Diaz, Guy
4 Habegger, Philipp
4 Jonsson, Mattias
3 Berenstein, Carlos Alberto
3 Bosser, Vincent
3 Bundschuh, Peter
3 Caveny, Deanna M.
3 Chardin, Marc
3 Delaunay, Sandra
3 Favre, Charles
3 Fischler, Stéphane
3 Gramain, Francois
3 Gun, Sanoli
3 Heintz, Joos
3 Hirata-Kohno, Noriko
3 Jeronimo, Gabriela
3 Laurent, Michel
3 Morais, Jose Enrique
3 Moriwaki, Atsushi
3 Pazuki, Fabien
3 Pellarin, Federico
3 Pontreau, Corentin
3 Ratazzi, Nicolas
3 Rath, Purusottam
3 Schmidt, Wolfgang M.
3 Töpfer, Thomas
3 Väänänen, Keijo O.
3 Wüstholz, Gisbert
3 Yger, Alain
3 Zannier, Umberto M.
3 Zorin, Evgeniy V.
2 Adamczewski, Boris
2 Autissier, Pascal
2 Bainbridge, Matt
2 Bertrand, Daniel
2 Bombieri, Enrico
2 Boxall, John L.
2 Bugeaud, Yann
2 Chambert-Loir, Antoine
2 Checcoli, Sara
2 Denis, Laurent
2 Dill, Gabriel A.
2 Elsner, Carsten
2 Fernandes, Gwladys
2 Gao, Xiaoshan
2 Giusti, Marc
2 Hägele, Klemens
2 Hajli, Mounir
2 Kholyavka, Yaroslav M.
2 Künnemann, Klaus
2 Langevin, Michel
2 Li, Yinghong
2 Liţcanu, Răzvan
2 Martin, Florent
2 Martínez, César E.
2 Möller, Martin
2 Pintér, Ákos
2 Shiokawa, Iekata
2 Solernó, Pablo
2 Veneziano, Francesco
1 Abbes, Ahmed
1 Aleksentsev, Yu. M.
1 Almeida, Marcela
1 Amou, Masaaki
1 Andersen, Nickolas
1 Aschenbrenner, Matthias
1 Ascher, Kenneth
1 Avendano, Martin
1 Ballaÿ, François
1 Bartolome, Boris
1 Basu, Saugata
1 Becker, Paul-Georg
1 Bennett, Curtis D.
1 Bérczes, Attila
1 Bilu, Yuri F.
1 Binyamini, Gal
1 Blass, Jozef
1 Blaum, Manuela
...and 127 more Authors
all top 5

Cited in 86 Serials

18 Journal of Number Theory
17 Journal de Théorie des Nombres de Bordeaux
13 Transactions of the American Mathematical Society
12 Inventiones Mathematicae
11 Annales de l’Institut Fourier
11 Compositio Mathematica
11 Mathematische Annalen
9 International Journal of Number Theory
8 Comptes Rendus. Mathématique. Académie des Sciences, Paris
7 Bulletin de la Société Mathématique de France
6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
6 Journal of Algebra
6 Journal für die Reine und Angewandte Mathematik
6 Proceedings of the American Mathematical Society
6 The Ramanujan Journal
5 Journal of the American Mathematical Society
5 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV
4 Duke Mathematical Journal
4 Journal of Pure and Applied Algebra
4 Mathematische Zeitschrift
4 Monatshefte für Mathematik
4 Journal of Complexity
4 Algebra & Number Theory
3 Bulletin of the Australian Mathematical Society
3 Mathematics of Computation
3 Expositiones Mathematicae
3 Indagationes Mathematicae. New Series
3 Applicable Algebra in Engineering, Communication and Computing
3 Journal of Algebraic Geometry
3 Documenta Mathematica
3 Foundations of Computational Mathematics
2 Journal d’Analyse Mathématique
2 Rocky Mountain Journal of Mathematics
2 Acta Mathematica
2 Functiones et Approximatio. Commentarii Mathematici
2 Publications Mathématiques
2 Manuscripta Mathematica
2 Mathematika
2 Proceedings of the Japan Academy. Series A
2 Advances in Applied Mathematics
2 Discrete & Computational Geometry
2 Séminaire de Théorie des Nombres de Bordeaux. Deuxième Série
2 Mémoires de la Société Mathématique de France. Nouvelle Série
2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V
2 Kyoto Journal of Mathematics
2 Journal de l’École Polytechnique – Mathématiques
1 Communications in Algebra
1 Israel Journal of Mathematics
1 Mathematical Notes
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Moscow University Mathematics Bulletin
1 The Mathematical Intelligencer
1 Beiträge zur Algebra und Geometrie
1 Acta Arithmetica
1 Advances in Mathematics
1 Canadian Journal of Mathematics
1 Dissertationes Mathematicae
1 Journal of Combinatorial Theory. Series A
1 Journal of Computational and Applied Mathematics
1 Memoirs of the American Mathematical Society
1 Proceedings of the London Mathematical Society. Third Series
1 Rendiconti del Seminario Matematico della Università di Padova
1 Annales de la Faculté des Sciences de Toulouse. Série V. Mathématiques
1 Acta Mathematica Hungarica
1 Journal of Symbolic Computation
1 International Journal of Mathematics
1 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
1 Computational Mathematics and Mathematical Physics
1 Aequationes Mathematicae
1 L’Enseignement Mathématique. 2e Série
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Russian Journal of Mathematical Physics
1 Journal of Mathematical Sciences (New York)
1 Annales Mathématiques Blaise Pascal
1 Selecta Mathematica. New Series
1 Electronic Research Announcements of the American Mathematical Society
1 Acta Mathematica Sinica. English Series
1 Bulletin of the Brazilian Mathematical Society. New Series
1 Mathematics in Computer Science
1 Complex Analysis and Operator Theory
1 Forum of Mathematics, Sigma
1 Carpathian Mathematical Publications
1 Mathematics
1 Research in Number Theory
1 Algebraic Combinatorics

Citations by Year