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Date: 14-12-2019
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Date: 13-9-2020
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Date: 14-7-2020
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Let , ..., for be a set of E-functions that (1) form a solution of the system of differential equations
for and , ..., and (2) are algebraically independent over . Then for all , where denotes the set of algebraic numbers with and distinct from singularities of the differential equations, the numbers , ..., are algebraically independent (Nesterenko 1999).
REFERENCES:
Nesterenko, Yu. V. A Course on Algebraic Independence: Lectures at IHP 1999. Unpublished manuscript. 1999.
Shidlovskii, A. B. Transcendental Numbers. New York: de Gruyter, 1989.
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