On p-adic differential equations. The Frobenius structure of differential equations
Table ronde d'analyse non archimédienne (Paris, 1972), Mémoires de la Société Mathématique de France, no. 39-40 (1974), pp. 27-37.
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Dwork, B. M. On $p$-adic differential equations. The Frobenius structure of differential equations, dans Table ronde d'analyse non archimédienne (Paris, 1972), Mémoires de la Société Mathématique de France, no. 39-40 (1974), pp. 27-37. doi : 10.24033/msmf.161. http://www.numdam.org/articles/10.24033/msmf.161/

[1] Dwork, B. "A deformation theory for the zeta function of a hypersurface" Proc. Int'1. Cong. Math., Stockholm 1962 pp. 247-259. | Zbl

[2] Dwork, B. "On the zeta function of a hypersurface II, Annals of Math. 80 (1964) pp. 227-299. | MR

[3] Dwork, B. "p-adic cycles" Publ. Math. IHES 37, Paris, 1969, pp. 27-116. | Numdam | MR | Zbl

[4] Dwork, B. "On p-adic differential equations II", Annals of Math., to appear.

[5] Dwork, B. "On p-adic differential equations III", submitted to Inventiones Math. | Zbl

[6] Katz, N. "Travaux de Dwork" exposé 409, Seminaire Bourbaki 1972. | Numdam | Zbl

[7] Turrittin, H.L. "Convergent solutions of ordinary linear homogeneous differential equations in the neighbourhood of an irregular singular point" Acta Math. 93 (1955) pp. 27-66. | MR | Zbl

[8] Wasow, W. "Asymptotic expansions for ordinary differential equations" Interscience Publishers, New York 1965. | MR | Zbl

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