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Nearly perfect systems and effective generalizations of Shidlovski’s theorem. (English) Zbl 0469.10010


MSC:

11J81 Transcendence (general theory)
11J85 Algebraic independence; Gel’fond’s method
34A30 Linear ordinary differential equations and systems
12H05 Differential algebra
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[1] Nesterenko, Ju.V, Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers, Math. USSR izv., 2, No. 2, 239-270, (1977), [English transl.] · Zbl 0378.10022
[2] Mahler, K, ()
[3] Mahler, K, Perfect systems, Compositio math., 19, 95-116, (1968) · Zbl 0168.31303
[4] Baum, L.E; Sweet, M.M, Continued fractions of algebraic power series in characteristic 2, Ann. of math., 103, 593-610, (1976) · Zbl 0312.10024
[5] Cope, F.T, Formal solutions of irregular linear differential equations, I, Amer. J. math., 56, 411-437, (1934) · Zbl 0009.35401
[6] Rabin, M.O, Computable algebra, general theory and theory of computable fields, Trans. amer. math. soc., 95, 341-360, (1960) · Zbl 0156.01201
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