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On Siegel–Shidlovskii’s theory for $$q$$-difference equations. (English) Zbl 1113.11042
Following A. B. Shidlovski [Transcendental numbers.De Gruyter Studies in Mathematics, 12. Berlin etc.: Walter de Gruyter (1989; Zbl 0689.10043)], the authors modify his theory of E-functions to the theory of $$q$$-differences. In this spirit they receive very interesting results concerning the linear independence and measure of linear independence. The main proofs are based on the analogue of Siegel’s lemma and make also use of Padé type approximations.

##### MSC:
 11J82 Measures of irrationality and of transcendence 11J72 Irrationality; linear independence over a field 39A13 Difference equations, scaling ($$q$$-differences)
##### Keywords:
measure of linear independence; difference equations
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