Comptes Rendus
no. 5-6
Number Theory
An algorithm computing non-solvable spectral radii of p-adic differential equations
[Un algorithme pour le calcul des rayons de convergence non solubles des équations différentielles p-adiques]

Présenté par : the Editorial Board

Andrea Pulita1
1 Département de mathématiques, université Montpellier-2, CC051, place Eugène-Bataillon, 34095, Montpellier cedex 5, France
Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 167-171.

Nous obtenons un algorithme pour le calcul explicite des valeurs des rayons de convergence spectrales non solubles des solutions dʼun module différentiel sur un point de type 2, 3 ou 4 de la droite affine de Berkovich.

We obtain an algorithm computing explicitly the values of the non-solvable spectral radii of convergence of the solutions of a differential module over a point of type 2, 3 or 4 of the Berkovich affine line.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.02.017
Andrea Pulita 1

1 Département de mathématiques, université Montpellier-2, CC051, place Eugène-Bataillon, 34095, Montpellier cedex 5, France 
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Andrea Pulita. An algorithm computing non-solvable spectral radii of p-adic differential equations. Comptes Rendus. Mathématique, Volume 351 (2013) no. 5-6, pp. 167-171. doi : 10.1016/j.crma.2013.02.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.02.017/

[1] Gilles Christol, Structure de Frobénius des équations différentielles p-adiques, in: Groupe dʼÉtude dʼAnalyse Ultramétrique, 3e année (1975/1976), Fasc. 2, Marseille-Luminy, 1976, Exp. No. J5, Secrétariat Math., Paris, 1977, p. 7, MR 0498578 (58#16673).

[2] Gilles Christol The radius of convergence function for first order differential equations, Advances in Non-Archimedean Analysis, Contemp. Math., vol. 551, Amer. Math. Soc., Providence, RI, 2011, pp. 71-89 (MR 2882390)

[3] G. Christol; B. Dwork Modules différentiels sur des couronnes, Ann. Inst. Fourier (Grenoble), Volume 44 (1994) no. 3, pp. 663-701 MR MR1303881 (96f:12008)

[4] Pierre Deligne Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer-Verlag, Berlin, 1970 MR MR0417174 (54#5232)

[5] Nicholas M. Katz A simple algorithm for cyclic vectors, Amer. J. Math., Volume 109 (1987) no. 1, pp. 65-70 MR MR878198 (88b:13001)

[6] Kiran S. Kedlaya p-Adic Differential Equations, Cambridge Stud. Adv. Math., vol. 125, Cambridge Univ. Press, 2010

[7] Andrea Pulita, Small connections are cyclic, available at http://www.math.univ-montp2.fr/~pulita/Publications/Small-Connections.pdf.

[8] Andrea Pulita Rank one solvable p-adic differential equations and finite abelian characters via Lubin–Tate groups, Math. Ann., Volume 337 (2007) no. 3, pp. 489-555 (MR MR2274542)

[9] Andrea Pulita, The convergence Newton polygon of a p-adic differential equation I: Affinoid domains of the Berkovich affine line, preprint, 2012, 44 pp., . | arXiv

[10] Paul Thomas Young Radii of convergence and index for p-adic differential operators, Trans. Amer. Math. Soc., Volume 333 (1992) no. 2, pp. 769-785 MR 1066451 (92m:12015)

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