Edit Profile (opens in new tab) Rond, Guillaume Co-Author Distance Author ID: rond.guillaume Published as: Rond, Guillaume; Rond, G. Homepage: http://www.i2m.univ-amu.fr/perso/guillaume.rond/ External Links: MGP · IdRef · theses.fr Documents Indexed: 41 Publications since 2003, including 8 Additional arXiv Preprints Reviewing Activity: 35 Reviews Co-Authors: 14 Co-Authors with 18 Joint Publications 242 Co-Co-Authors all top 5 Co-Authors 23 single-authored 5 Parusiński, Adam 3 Aroca, Fuensanta 3 Belotto da Silva, André Ricardo 3 Curmi, Octave 3 Decaup, Julie 2 Bilski, Marcin 2 Popescu, Dorin 1 Castro-Jiménez, Francisco Jesús 1 Hickel, Michel 1 Kurdyka, Krzysztof 1 Lamel, Bernhard 1 Mir, Nordine 1 Schober, Bernd 1 Spivakovsky, Mark all top 5 Serials 4 Journal of Algebra 3 Proceedings of the American Mathematical Society 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Journal of Singularities 1 Communications in Algebra 1 Advances in Mathematics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Canadian Mathematical Bulletin 1 Commentarii Mathematici Helvetici 1 Journal of the London Mathematical Society. Second Series 1 Journal of Pure and Applied Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Osaka Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Transactions of the American Mathematical Society 1 Journal of Algebraic Geometry 1 Mathematical Research Letters 1 Algebra & Number Theory 1 Journal de l’École Polytechnique – Mathématiques all top 5 Fields 27 Commutative algebra (13-XX) 25 Algebraic geometry (14-XX) 19 Several complex variables and analytic spaces (32-XX) 7 Number theory (11-XX) 6 Field theory and polynomials (12-XX) 3 Mathematical logic and foundations (03-XX) 2 Combinatorics (05-XX) 2 Associative rings and algebras (16-XX) 2 Real functions (26-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 22 Publications have been cited 83 times in 53 Documents Cited by ▼ Year ▼ The Abhyankar-Jung theorem. Zbl 1268.13008 Parusiński, Adam; Rond, Guillaume 15 2012 Artin approximation. Zbl 1396.13001 Rond, Guillaume 13 2018 On the linearity of Artin functions. (Sur la linéarité de la fonction de Artin.) Zbl 1109.14006 Rond, Guillaume 8 2005 Local topological algebraicity of analytic function germs. Zbl 1365.32005 Bilski, Marcin; Parusiński, Adam; Rond, Guillaume 8 2017 Homomorphisms of local algebras in positive characteristic. Zbl 1189.13022 Rond, Guillaume 4 2009 Diophantine approximation in power series fields of several variables. (Approximation diophantienne dans les corps de séries en plusieurs variables.) Zbl 1126.11035 Rond, Guillaume 4 2006 Artin-Rees Lemma, Izumi theorem and Artin function. (Lemme d’Artin-Rees, théorème d’Izumi et fonction de Artin.) Zbl 1099.13017 Rond, Guillaume 4 2006 The analogue of Izumi’s theorem for Abhyankar valuations. Zbl 1318.13007 Rond, G.; Spivakovsky, M. 4 2014 Linear nested Artin approximation theorem for algebraic power series. Zbl 1403.13014 Castro-Jiménez, Francisco-Jesús; Popescu, Dorin; Rond, Guillaume 4 2019 Effective bounds of functions approximating formal solutions of binomial equations. (Bornes effectives des fonctions d’approximation des solutions formelles d’équations binomiales.) Zbl 1200.13016 Rond, Guillaume 2 2010 Higher order approximation of analytic sets by topologically equivalent algebraic sets. Zbl 1393.32012 Bilski, Marcin; Kurdyka, Krzysztof; Parusiński, Adam; Rond, Guillaume 2 2018 Cylindric Artin approximation and homomorphisms of analytic algebras. (Approximation de Artin cylindrique et morphismes d’algèbres analytiques.) Zbl 1159.13005 Rond, Guillaume 2 2008 Algebraic varieties are homeomorphic to varieties defined over number fields. Zbl 1454.14147 Parusiński, Adam; Rond, Guillaume 2 2020 Approximation of holomorphic solutions of a system of real analytic equations. Zbl 1259.13005 Hickel, Michel; Rond, Guillaume 2 2012 Local topological algebraicity with algebraic coefficients of analytic sets or functions. Zbl 1400.32014 Rond, Guillaume 2 2018 Motivic Poincaré series of a quasi-ordinary irreducible germ of hypersurface. (Séries de Poincaré motiviques d’un germe d’hypersurface irréductible quasi-ordinaire.) Zbl 1190.14008 Rond, Guillaume 1 2009 An irreducibility criterion for power series. Zbl 1375.13027 Rond, Guillaume; Schober, Bernd 1 2017 Local zero estimates and effective division in rings of algebraic power series. Zbl 1411.13035 Rond, Guillaume 1 2018 About the Artin function in dimension \(N\geqslant 2\). (A propos de la fonction de Artin en dimension \(N\geqslant 2\).) Zbl 1071.14005 Rond, Guillaume 1 2005 About the algebraic closure of the field of power series in several variables in characteristic zero. Zbl 1360.13052 Rond, Guillaume 1 2017 Support of Laurent series algebraic over the field of formal power series. Zbl 1419.13039 Aroca, Fuensanta; Rond, Guillaume 1 2019 Łojasiewicz inequality over the ring of power series in two variables. Zbl 1286.14076 Rond, Guillaume 1 2013 Algebraic varieties are homeomorphic to varieties defined over number fields. Zbl 1454.14147 Parusiński, Adam; Rond, Guillaume 2 2020 Linear nested Artin approximation theorem for algebraic power series. Zbl 1403.13014 Castro-Jiménez, Francisco-Jesús; Popescu, Dorin; Rond, Guillaume 4 2019 Support of Laurent series algebraic over the field of formal power series. Zbl 1419.13039 Aroca, Fuensanta; Rond, Guillaume 1 2019 Artin approximation. Zbl 1396.13001 Rond, Guillaume 13 2018 Higher order approximation of analytic sets by topologically equivalent algebraic sets. Zbl 1393.32012 Bilski, Marcin; Kurdyka, Krzysztof; Parusiński, Adam; Rond, Guillaume 2 2018 Local topological algebraicity with algebraic coefficients of analytic sets or functions. Zbl 1400.32014 Rond, Guillaume 2 2018 Local zero estimates and effective division in rings of algebraic power series. Zbl 1411.13035 Rond, Guillaume 1 2018 Local topological algebraicity of analytic function germs. Zbl 1365.32005 Bilski, Marcin; Parusiński, Adam; Rond, Guillaume 8 2017 An irreducibility criterion for power series. Zbl 1375.13027 Rond, Guillaume; Schober, Bernd 1 2017 About the algebraic closure of the field of power series in several variables in characteristic zero. Zbl 1360.13052 Rond, Guillaume 1 2017 The analogue of Izumi’s theorem for Abhyankar valuations. Zbl 1318.13007 Rond, G.; Spivakovsky, M. 4 2014 Łojasiewicz inequality over the ring of power series in two variables. Zbl 1286.14076 Rond, Guillaume 1 2013 The Abhyankar-Jung theorem. Zbl 1268.13008 Parusiński, Adam; Rond, Guillaume 15 2012 Approximation of holomorphic solutions of a system of real analytic equations. Zbl 1259.13005 Hickel, Michel; Rond, Guillaume 2 2012 Effective bounds of functions approximating formal solutions of binomial equations. (Bornes effectives des fonctions d’approximation des solutions formelles d’équations binomiales.) Zbl 1200.13016 Rond, Guillaume 2 2010 Homomorphisms of local algebras in positive characteristic. Zbl 1189.13022 Rond, Guillaume 4 2009 Motivic Poincaré series of a quasi-ordinary irreducible germ of hypersurface. (Séries de Poincaré motiviques d’un germe d’hypersurface irréductible quasi-ordinaire.) Zbl 1190.14008 Rond, Guillaume 1 2009 Cylindric Artin approximation and homomorphisms of analytic algebras. (Approximation de Artin cylindrique et morphismes d’algèbres analytiques.) Zbl 1159.13005 Rond, Guillaume 2 2008 Diophantine approximation in power series fields of several variables. (Approximation diophantienne dans les corps de séries en plusieurs variables.) Zbl 1126.11035 Rond, Guillaume 4 2006 Artin-Rees Lemma, Izumi theorem and Artin function. (Lemme d’Artin-Rees, théorème d’Izumi et fonction de Artin.) Zbl 1099.13017 Rond, Guillaume 4 2006 On the linearity of Artin functions. (Sur la linéarité de la fonction de Artin.) Zbl 1109.14006 Rond, Guillaume 8 2005 About the Artin function in dimension \(N\geqslant 2\). (A propos de la fonction de Artin en dimension \(N\geqslant 2\).) Zbl 1071.14005 Rond, Guillaume 1 2005 all cited Publications top 5 cited Publications all top 5 Cited by 56 Authors 16 Rond, Guillaume 7 Parusiński, Adam 5 Popescu, Dorin 3 Gryszka, Beata 3 Kerner, Dmitry 3 Lamel, Bernhard 3 Paunescu, Laurentiu 2 Aroca, Fuensanta 2 Belitskii, Genrich R. 2 Boix, Alberto Fernandez 2 Cutkosky, Steven Dale 2 Datta, Rankeya 2 Decaup, Julie 2 González Pérez, Pedro Daniel 2 Greuel, Gert-Martin 2 Gwoździewicz, Janusz 2 Hickel, Michel 2 McCallum, Scott 2 Mir, Nordine 2 Spivakovsky, Mark 1 Adamus, Janusz 1 Beddani, Charef 1 Belotto da Silva, André Ricardo 1 Bilski, Marcin 1 Bostan, Alin 1 Budur, Nero 1 Castro-Jiménez, Francisco Jesús 1 Cobo Pablos, Helena 1 Curmi, Octave 1 Dinh, Trung T. 1 Ferrarotti, Massimo 1 Fortuna, Elisabetta 1 García Barroso, Evelia Rosa 1 Hauser, Herwig 1 Hong, Hoon 1 Huneke, Craig L. 1 Ito, Hirotada 1 Izumi, Shuzo 1 Katz, Daniel 1 Khalid, Asma 1 Kosar, Zunaira 1 Kossovskiy, Il’ya Grigor’evich 1 Kurdyka, Krzysztof 1 Notarantonio, Hadrien 1 Nowak, Krzysztof Jan 1 Pfister, Gerhard 1 Pham, Thuy Huong 1 Popescu-Pampu, Patrick 1 Saavedra, Víctor Manuel 1 Safey El Din, Mohab 1 Schober, Bernd 1 Stolovitch, Laurent 1 Villa, Manuel González 1 Wang, Botong 1 Wilson, Leslie Charles 1 Yurkevich, Sergey V. all top 5 Cited in 29 Serials 5 Journal of Pure and Applied Algebra 4 Advances in Mathematics 4 Transactions of the American Mathematical Society 3 Journal of Algebra 2 Communications in Algebra 2 Annales de l’Institut Fourier 2 Mathematische Zeitschrift 2 Proceedings of the American Mathematical Society 2 Journal of Symbolic Computation 2 Journal of Algebraic Geometry 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Algebra & Number Theory 2 Journal of Singularities 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Rocky Mountain Journal of Mathematics 1 Annales Polonici Mathematici 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Colloquium Mathematicum 1 Commentarii Mathematici Helvetici 1 Dissertationes Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Osaka Journal of Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Algebra and its Applications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 European Journal of Mathematics 1 Journal de l’École Polytechnique – Mathématiques all top 5 Cited in 17 Fields 38 Algebraic geometry (14-XX) 32 Commutative algebra (13-XX) 18 Several complex variables and analytic spaces (32-XX) 6 Field theory and polynomials (12-XX) 4 Mathematical logic and foundations (03-XX) 3 Associative rings and algebras (16-XX) 3 Computer science (68-XX) 2 Combinatorics (05-XX) 2 Number theory (11-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Difference and functional equations (39-XX) 2 Operator theory (47-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Numerical analysis (65-XX) Citations by Year