Shidlovskii Theorem
المؤلف:
Nesterenko, Yu. V.
المصدر:
A Course on Algebraic Independence: Lectures at IHP 1999. Unpublished manuscript. 1999.
الجزء والصفحة:
...
2-2-2021
2477
Shidlovskii Theorem
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 Unpublished manuscript. 1999.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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