Articles et preprints

Edition

(with Guy Casale and Jean-Pierre Ramis) Volume à la mémoire de Hiroshi Umemura : “Équations de Painlevé et théories de Galois différentielles”, Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020).

(with Tanguy Rivoal) "Arithmetic and Galois theories of differential equations". Séminaires et Congrès 23 (2011).

Preprints

24. (with Gwladys Fernandes and Marni Mishna) Inhomogeneous order 1 iterative functional equations with applications to combinatorics. 26 pages.

23. (with Gwladys Fernandes) A Galoisian proof of Ritt theorem on the differential transcendence of Poincaré functions. 6 pages.

Articles in press 

22. (with Alin Bostan and Kilian Rachel) Differential transcendence of Bell numbers and relatives: a Galois theoretic approach. 20 pages, to appear in American Journal of Mathematics.  

Publications

21.(with Charlotte Hardouin)  Intrinsic approach to Galois theory of q-difference equations, with a preface to Part IV by Anne Granier.  Memoirs of the American Mathematical Society, 2022, vol. 279, n. 1376.

20. Difference Galois theory for the "applied" mathematician, lecture notes from the cours given at VIASM school on Number Theory (18-24/06/2018, Hanoi, Vietnam). To appear in "Arithmetic and geometry over local fields", Lecture Notes in Mathematics 2275, 2021, Springer.

19. (with Charlotte Hardouin) Galois theories for q-difference equations: comparison theorems. Confluentes Mathematici, Tome 12 (2020) no. 2, pp. 11-35.

18.  (with Moulay A. Barkatou, Thomas Cluzeau, Jacques-Arthur Weil) Reduced forms of linear differential systems and the intrinsic Galois-Lie algebra of Katz. SIGMA 16 (2020), 054, 13 pages.

17. Action of an endomorphism on (the solutions of) a linear differential equation. Proceedings of the conference Analogies between number field and function field: algebraic and analytic approaches, 27/06-01/07/2016, Lyon. Publications Mathématiques de Besançon no. 1 (2019), 21-39.

16. (with Charlotte Hardouin and Michael Wibmer) Difference algebraic relations among solutions of linear differential equations. Journal of the Institute of Mathematics of Jussieu, 16 (2017), No. 1, 59-119.

15. (with Moulay A. Barkatou, Thomas Cluzeau, Jacques-Arthur Weil) Computing the Lie Algebra of the Differential Galois Group of a Linear Differential System. Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation (ISSAC), 63–70. 

14. (with Charlotte Hardouin and Michael Wibmer) Difference Galois theory of linear differential equations. Advances in Mathematics, 260 (2014), 1--58.

13. Approche galoisienne de la transcendance différentielle. Journée annuelle 2012 de la SMF. 20 pages.

12. (with Charlotte Hardouin) Descent for differential Galois theory of difference equations. Confluence and q-dependency. Pacific Journal of Mathematics, Vol. 256 (2012), No. 1, 79--104.

11. (with Jacques Sauloy) Outils pour la classification locale des équations aux q-différences linéaires complexes. Séminaires et Congrès 23 (2011), 229-282.

10. (with Charlotte Hardouin) Courbures, groupes de Galois génériques et D-groupoïdes de Galois d'un système aux q-différences. C. R. Math. Acad. Sci. Paris 348 (2010), no. 17-18, 951--954.

9. Local analytic classification of q-difference equations with |q|=1. Journal of Noncommutative Geometry, 3(1), 2009, 125--149.

8. (with Changgui Zhang) On q-summation and confluence. Annales de l'Institut Fourier, 59 no.1 (2009), 347-392. 

7. An ultrametric version of the Maillet-Malgrange theorem for non linear q-difference equations. Proceedings of the American Mathematical Society, 136 (2008), 2803-2814.

6. (with Y. André) q-difference equations and p-adic local monodromy. Astérisque 296(2004), 55--111.

5. Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems). Geometric Aspects of Dwork's Theory, Vol. II, de Gruyter, 615--675.

4. (with J-P. Ramis, J. Sauloy, Ch. Zhang) Equations aux q-différences. Gazette des mathématiciens, no. 96 (2003), 20--49.

3. On the arithmetic theory of q-difference equations. The q-analogue of the Grothendieck-Katz's conjecture on p-curvatures. Inventiones Mathematicae 150 (2002) 3, 517--578. 

2. Sur la théorie géométrique des G-fonctions (Le théorème de Chudnovsky à plusieurs variables). Mathematische Annalen 319 (2001) 1, 181--213

1. On arithmetic size of linear differential equation. Journal of Algebra 242 (2001) 1, 31--59.

Unpublished preprints

"Arithmetic theory of q-difference equations (G_q-functions and q-difference modules of type G, global q-Gevrey series)". ArXiv:0902.4169.

(with F. Baldassarri) "Continuity of the radius of convergence of p-adic differential equations on Berkovich analytic spaces". Preprint, 25 pages. ArXiv: 0709.2008. The article by F. Baldassarri "Continuity of the radius of convergence of differential equations on p-adic analytic curves", Invent. Math. 182 (2010), no. 3, 513–584 improves the results of the paper above (which is in several variables) in the case of meromorphic connections on an analytic curve.

Other mathematical texts