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In the recent years, the nature of the generating series of walks in the quarter plane has attracted the attention of many authors in combinatorics and probability. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least hyperalgebraic (solutions of algebraic differential equations)? In this talk, we will show how the nature of the generating function can be approached via the study of a discrete functional equation over a curve E, of genus zero or one. In the first case, the functional equation corresponds to a so called q-difference equation and all the related generating series are differentially transcendental. For the genus one case, the dynamic of the functional equation corresponds to the addition by a given point P of the elliptic curve E. In that situation, one can relate the nature of the generating series to the fact that the point P is of torsion or not. In the recent years, the nature of the generating series of walks in the quarter plane has attracted the attention of many authors in combinatorics and probability. The main questions are: are they algebraic, holonomic (solutions of linear differential equations) or at least hyperalgebraic (solutions of algebraic differential equations)? In this talk, we will show how the nature of the generating function can be approached via the study of a ...

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Documents 12F10 | enregistrements trouvés : 59

Galois theory and walks in the quarter plane Hardouin, Charlotte | CIRM H Nouveau

Galois codes for arithmetic and geometry via the power of valuation theory Koenigsmann, Jochen | CIRM H Nouveau

Topics in algebraic and noncommutative geometry :proceedings in memory of Ruth Michler held at CIRM#Luminy#July 20-22#Oct. 25-28 Melles, Caroline Grant ; Brasselet, Jean-Paul ; Kennedy, Gary ; Lauter, Kristin | American Mathematical Society 2003 Nouveau

Séminaire Bourbaki. Vol. 2002/2003 :exposés 909-923 | Société Mathématique de France 2003 Nouveau

Model theory and applications:based on the Euro-conference in model theory and applicationsRavello # may 27 - june 1, 2002 Bélair, L. ; Chatzidakis, Z. ; D'Aquino, P. ; Marker, D. ; Otero, M. ; Point, F. ; Wilkie, A. | ARACNE 2002 Nouveau

Geometric and differential Galois theories.Proceedings of the meeting at CIRMMarseille # march 29 - april 2, 2010 Bertrand, D. ; Boalch, Ph. ; Couveignes, J.-M. ; Dèbes, P. | Société Mathématique de France 2013 Nouveau

Valuation theory in interaction.Proceedings of the 2nd international conference and workshop on valuation theorySegovia and El Escorial # July 18-29, 2011 Campillo, Antonio ; Kuhlmann, Franz-Viktor ; Teissier, Bernard | European Mathematical Society 2014 Nouveau

Algebraic groups: structure ans actions.2015 Clifford lectures on algebraic groups: structure and actionsNew Orleans # March 2-5, 2015 Can, Mahir Bilen | American Mathematical Society 2017 Nouveau

Recent progress in the classification of torsion subgroups of elliptic curves Lozano-Robledo, Alvaro | CIRM H Nouveau

Konstruktive galoistheorie Matzat, B. Heinrich | Springer-Verlag 1987 Nouveau

Topics in field theory Karpilovsky, Gregory | North-Holland 1989 Nouveau

Galois' theory of algebraic equations Tignol, Jean-Pierre ; Blyth, T. S. | Longman Scientific And Technical 1988 Nouveau

Galois theory Rotman, Joseph | Springer-Verlag 1990 Nouveau

A course in galois theory Garling, D. J. H. | Cambridge University Press 1991 Nouveau

Introduction to field theory Adamson, Iain T. | Oliver & Boyd 1964 Nouveau

Les structures fondamentales de l'analyse première partieLivre II algèbre chapitre 4 et 5polynomes et fractions rationnelles, corps commutatifs Bourbaki, N. | Hermann & Cie. 1950 Nouveau

Uber die darstellung von gruppen in galoisschen feldern Brauer, Richard | Hermann & Cie. 1935 Nouveau

Galois' Dream :group theory and differential equations Kuga, Michio ; Addington, Susan ; Mulase, Motohico | Birkhäuser 1993 Nouveau

Rings, fields and groupsan introduction to abstract algebra Allenby, R. B. J. T. | Edward Arnold 1991 Nouveau

Fields and rings Kaplansky, Irving | The University of Chicago Press 1969 Nouveau

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Topics in algebraic and noncommutative geometry :
proceedings in memory of Ruth Michler held at CIRM#Luminy#July 20-22#Oct. 25-28 Melles, Caroline Grant ; Brasselet, Jean-Paul ; Kennedy, Gary ; Lauter, Kristin | American Mathematical Society 2003 Nouveau

Séminaire Bourbaki. Vol. 2002/2003 :
exposés 909-923 | Société Mathématique de France 2003 Nouveau

Model theory and applications:
based on the Euro-conference in model theory and applications
Ravello # may 27 - june 1, 2002 Bélair, L. ; Chatzidakis, Z. ; D'Aquino, P. ; Marker, D. ; Otero, M. ; Point, F. ; Wilkie, A. | ARACNE 2002 Nouveau

Geometric and differential Galois theories.
Proceedings of the meeting at CIRM
Marseille # march 29 - april 2, 2010 Bertrand, D. ; Boalch, Ph. ; Couveignes, J.-M. ; Dèbes, P. | Société Mathématique de France 2013 Nouveau

Valuation theory in interaction.
Proceedings of the 2nd international conference and workshop on valuation theory
Segovia and El Escorial # July 18-29, 2011 Campillo, Antonio ; Kuhlmann, Franz-Viktor ; Teissier, Bernard | European Mathematical Society 2014 Nouveau

Algebraic groups: structure ans actions.
2015 Clifford lectures on algebraic groups: structure and actions
New Orleans # March 2-5, 2015 Can, Mahir Bilen | American Mathematical Society 2017 Nouveau

Les structures fondamentales de l'analyse première partie
Livre II algèbre chapitre 4 et 5
polynomes et fractions rationnelles, corps commutatifs Bourbaki, N. | Hermann & Cie. 1950 Nouveau

Galois' Dream :
group theory and differential equations Kuga, Michio ; Addington, Susan ; Mulase, Motohico | Birkhäuser 1993 Nouveau

Rings, fields and groups
an introduction to abstract algebra Allenby, R. B. J. T. | Edward Arnold 1991 Nouveau