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.
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.
Accepted:
Published online:
@article{CRMATH_2013__351_5-6_167_0, author = {Pulita, Andrea}, title = {An algorithm computing non-solvable spectral radii of \protect\emph{p}-adic differential equations}, journal = {Comptes Rendus. Math\'ematique}, pages = {167--171}, publisher = {Elsevier}, volume = {351}, number = {5-6}, year = {2013}, doi = {10.1016/j.crma.2013.02.017}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2013.02.017/} }
TY - JOUR AU - Pulita, Andrea TI - An algorithm computing non-solvable spectral radii of p-adic differential equations JO - Comptes Rendus. Mathématique PY - 2013 SP - 167 EP - 171 VL - 351 IS - 5-6 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2013.02.017/ DO - 10.1016/j.crma.2013.02.017 LA - en ID - CRMATH_2013__351_5-6_167_0 ER -
%0 Journal Article %A Pulita, Andrea %T An algorithm computing non-solvable spectral radii of p-adic differential equations %J Comptes Rendus. Mathématique %D 2013 %P 167-171 %V 351 %N 5-6 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2013.02.017/ %R 10.1016/j.crma.2013.02.017 %G en %F CRMATH_2013__351_5-6_167_0
Pulita, Andrea. 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. http://archive.numdam.org/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] 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] Modules différentiels sur des couronnes, Ann. Inst. Fourier (Grenoble), Volume 44 (1994) no. 3, pp. 663-701 MR MR1303881 (96f:12008)
[4] Équations différentielles à points singuliers réguliers, Lecture Notes in Math., vol. 163, Springer-Verlag, Berlin, 1970 MR MR0417174 (54#5232)
[5] A simple algorithm for cyclic vectors, Amer. J. Math., Volume 109 (1987) no. 1, pp. 65-70 MR MR878198 (88b:13001)
[6] 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] 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] 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)
Cited by Sources: