I want to ask about references to papers, that probably exist, which explain the articles of Bernard Dwork starting from "The rationality of the zeta function of an algebraic variety" to "On the Boyarsky principle".
MR0498577 (58 #16672) Reviewed Katz, Nicholas Travaux de Dwork. (French. English summary) Séminaire Bourbaki, 24ème année (1971/1972), Exp. No. 409, pp. 167–200. Lecture Notes in Math., Vol. 317, Springer, Berlin, 1973.
Katz, Nicholas M.(1-PRIN); Tate, John(1-TX) Bernard Dwork (1923–1998). Notices Amer. Math. Soc. 46 (1999), no. 3, 338–343. 0
You could start with the book by Dwork, Gerotto and Sullivan, "An introduction to G-functions", published by Princeton University Press in the collection Annals of math studies. It contains a full account of the rationality of the zeta function, and the beginnings of the study of p-adic differential equations.