Osgood, Charles F. Nearly perfect systems and effective generalizations of Shidlovski’s theorem. (English) Zbl 0469.10010 J. Number Theory 13, 515-540 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 3 Documents MSC: 11J81 Transcendence (general theory) 11J85 Algebraic independence; Gel’fond’s method 34A30 Linear ordinary differential equations and systems 12H05 Differential algebra Keywords:effective proof of Shidlovskij’s theorem; linear independence; linear forms; solution of linear differential system; partial differential operator PDF BibTeX XML Cite \textit{C. F. Osgood}, J. Number Theory 13, 515--540 (1981; Zbl 0469.10010) Full Text: DOI OpenURL References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.